{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":2311,"title":"Vector Magnitude Calculator","description":"'a' is a vector that starts at the origin and ends at (x, y). Find ||a||.\r\n\r\nHint: It is as simple as \"ABC\".","description_html":"\u003cp\u003e'a' is a vector that starts at the origin and ends at (x, y). Find \u003ctt\u003e|a|\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eHint: It is as simple as \"ABC\".\u003c/p\u003e","function_template":"function m = vector_magnitude(x, y)\r\n  m = x;\r\nend","test_suite":"%%\r\nx = 5;\r\ny = 12;\r\nmm = 13;\r\nassert(isequal(vector_magnitude(x, y),mm))\r\n\r\n%%\r\nx = 3;\r\ny = 4;\r\nmm = 5;\r\nassert(isequal(vector_magnitude(x, y),mm))\r\n\r\n%%\r\nx = 12;\r\ny = 35;\r\nmm = 37;\r\nassert(isequal(vector_magnitude(x, y),mm))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":26349,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":167,"test_suite_updated_at":"2014-06-05T15:55:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-07T19:54:35.000Z","updated_at":"2026-02-18T09:28:19.000Z","published_at":"2014-05-07T19:54:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'a' is a vector that starts at the origin and ends at (x, y). Find\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e|a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e|.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: It is as simple as \\\"ABC\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":685,"title":"Image Processing 2.1.1 Planck Integral","description":"Integrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\r\n\r\nPlanck  Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\r\n\r\nc1'=1.88365e23; % sec^-1 cm^-2 micron^3\r\n\r\nc2=1.43879e4;  % micron K\r\n\r\nMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\r\n\r\nRadiance  :    L = Me/pi in units of ph sec^-1 m^-2\r\n\r\nInput:  (3.0 5.0 250)  : From 3um to 5um at 250K\r\n\r\nOutput:  4.9612 E+018  : units ph/sec/m^2/ster\r\n\r\nPerformance Rqmts: \r\n\r\nAccuracy: \u003c0.001% error\r\n\r\nTime: \u003c100 msec (using cputime function)\r\n\r\n\r\nCorollary problem will include spectral transmission and emissivity.\r\n\r\n\r\nIR Calibration Reference:\r\n\r\n\u003chttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003e","description_html":"\u003cp\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/p\u003e\u003cp\u003ePlanck  Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/p\u003e\u003cp\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/p\u003e\u003cp\u003ec2=1.43879e4;  % micron K\u003c/p\u003e\u003cp\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/p\u003e\u003cp\u003eRadiance  :    L = Me/pi in units of ph sec^-1 m^-2\u003c/p\u003e\u003cp\u003eInput:  (3.0 5.0 250)  : From 3um to 5um at 250K\u003c/p\u003e\u003cp\u003eOutput:  4.9612 E+018  : units ph/sec/m^2/ster\u003c/p\u003e\u003cp\u003ePerformance Rqmts:\u003c/p\u003e\u003cp\u003eAccuracy: \u0026lt;0.001% error\u003c/p\u003e\u003cp\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/p\u003e\u003cp\u003eCorollary problem will include spectral transmission and emissivity.\u003c/p\u003e\u003cp\u003eIR Calibration Reference:\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\"\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/a\u003e\u003c/p\u003e","function_template":"function Radiance = Calc_Radiance(Lo,Hi,T)\r\n% Lo wavelength um\r\n% Hi wavelength um\r\n% T  Blackbody Temperature (K)\r\n\r\n  Radiance = T;\r\nend","test_suite":"%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=250.0;\r\n% Radiance = 4.96124998 e18 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.96124998e18; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=300.0;\r\n% Radiance = 4.1826971 e19 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.1826971e19; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=8.0;\r\nhi=12.0;\r\nT=280.0;\r\n% Radiance = 1.37122128 e21 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 1.37122128e21; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\n\r\n% Add random to block answer writers\r\nlo=3.0+rand\r\nhi=5.0+rand\r\nT=250.0;\r\n% Radiance = To be calculated ph/m2/sec/ster\r\n\r\nc1p=1.88365e23; % sec^-1cm^-2micron^3\r\nc2=1.43879e4;  % micron K\r\nsteps=1000;\r\n\r\nx=lo:(hi-lo)/steps:hi;\r\n\r\n% Planck Vectorized for Trapz\r\ny=1e8./(x.^4.*(exp(c2./(x.*T))-1));\r\n% Leading 1e8 is for numerical processing accuracy\r\n\r\nz=trapz(x,y);\r\nrad_correct=z*1e4*c1p/pi()/1e8 % 1e4 normalizes from cm-2 to m-2\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-14T04:31:21.000Z","updated_at":"2025-12-10T03:26:46.000Z","published_at":"2012-05-14T05:39:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec2=1.43879e4; % micron K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRadiance : L = Me/pi in units of ph sec^-1 m^-2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: (3.0 5.0 250) : From 3um to 5um at 250K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: 4.9612 E+018 : units ph/sec/m^2/ster\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePerformance Rqmts:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAccuracy: \u0026lt;0.001% error\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCorollary problem will include spectral transmission and emissivity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIR Calibration Reference:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":58259,"title":"Easy Sequences 115: Integral involving square root, floor, and round functions","description":"Given a postive real number , we are asked to evaluate the following integral:\r\n                            \r\n                            where:     the symbol \"\" is the floor function,\r\n                                            and \"\" is the round (to the nearest integer) function.\r\nWe may rewrite the above function in Matlab as:\r\n\u003e\u003e  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\r\nTherefore, for , we have:\r\n\u003e\u003e  s = S(10*pi)\r\ns =\r\n        12\r\nBe careful though, in using the Matlab integral function, as it is only an approximation. For example if :\r\n\u003e\u003e  s = S(100000)\r\n\r\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\r\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\r\nrequested accuracy. \r\n\u003e In integralCalc/iterateScalarValued (line 372)\r\nIn integralCalc/vadapt (line 132)\r\nIn integralCalc (line 75)\r\nIn integral (line 87)\r\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \r\n\r\ns =\r\n       49841\r\nThe correct answer is . The integral function is off by only 2 units here, but the discrepancy could be even greater for other values of . integral function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 673px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 445.71875px 336.5px; transform-origin: 445.71875px 336.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a postive real number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 48px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 24px; text-align: left; transform-origin: 384px 24px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-18px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"247.5\" height=\"48\" style=\"width: 247.5px; height: 48px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            where:     the symbol \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003efloor\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                            and \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/round.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eround \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(to the nearest integer) function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe may rewrite the above function in Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53\" height=\"18\" style=\"width: 53px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 30px; transform-origin: 442.71875px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(10*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBe careful though, in using the Matlab \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/integral.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efunction, as it is only an approximation. For example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"18\" style=\"width: 74px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 260px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 130px; transform-origin: 442.71875px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(100000)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eWarning: Reached the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003elimit on the maximum number of intervals in use. Approximate bound on error is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e8.0e+01. The integral \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003emay not exist\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e, or \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eit may be difficult to approximate numerically to the\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erequested \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eaccuracy. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt; In integralCalc/iterateScalarValued (line 372)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc/vadapt (line 132)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc (line 75)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegral (line 87)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e@(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       49841\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe correct answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"18\" style=\"width: 65px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n    % NOTE: the following expression is inaccurate for some values of n\r\n    s = round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n)); \r\nend","test_suite":"%%\r\nn = 1:20;\r\ns_correct = [0 0 0 1 1 1 2 2 3 3 3 4 4 5 6 6 6 7 7 7];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:20).*pi;\r\ns_correct = [1 2 3 4 6 7 8 11 11 12 15 16 17 18 20 22 23 24 26 28];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100*exp(1);\r\ns_correct = 126;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 1234.5678;\r\ns_correct = 601;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 12345.6789;\r\ns_correct = 6125;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100000;\r\ns_correct = 49839;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 6e6;\r\ns_correct = 2998571;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 4e8*pi;\r\ns_correct = 628304194;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 10.^(1:10);\r\ns_correct = 5555500618;\r\nassert(isequal(sum(arrayfun(@S,n)),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:1e5).*exp(2);\r\ns = arrayfun(@S,n);\r\nss = round([sum(s) nnz(s) mean(s) median(s) mode(s) std(s) sum(num2str(s))]);\r\nss_correct = [18444149135 100000 184441 184439 303161 106553 37072130];\r\nassert(isequal(ss,ss_correct))\r\nassert(isempty(lastwarn))","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-18T18:10:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2023-05-18T18:10:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-04T18:21:04.000Z","updated_at":"2023-05-18T18:10:26.000Z","published_at":"2023-05-05T19:51:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a postive real number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=S(n)=\\\\Bigg\\\\lfloor\\\\ \\\\int_0^n\\\\sqrt{\\\\lfloor{x}\\\\rfloor} - \\\\Big\\\\lfloor{\\\\sqrt{x} \\\\Big\\\\rfloor\\\\ \\\\mathrm{d}x\\\\  \\\\Bigg\\\\rceil \\\\cdot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            where:     the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e function,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            and \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/round.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eround \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e(to the nearest integer) function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe may rewrite the above function in Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  s = S(10*pi)\\ns =\\n        12]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBe careful though, in using the Matlab \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/integral.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003efunction, as it is only an approximation. For example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=100000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  s = S(100000)\\n\\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\\nrequested accuracy. \\n\u003e In integralCalc/iterateScalarValued (line 372)\\nIn integralCalc/vadapt (line 132)\\nIn integralCalc (line 75)\\nIn integral (line 87)\\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \\n\\ns =\\n       49841]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe correct answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=49839\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52328,"title":"ICFP2021 Hole-In-Wall: Figure Validation with Segment Crossing Check","description":"The ICFP held its annual 3-day contest in July 2021 with Hole-In-Wall. Contest Specification.\r\nThe contest folds the figure in Red to fit within the hole shown in light grey \r\nThis Challenge is to evaluate the complete Figure validation defined in the Specification when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\r\nValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u003c= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.  \r\nValid=check_figureS(hxy, pxy, mseg, epsilon, npxy)  \r\nCrossing Segments appears in Cody 1720 but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\r\nThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use Register Team. Anyone can select Problems Page and then click problem numbers to see the puzzles and to download problem files.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 669px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 334.5px; transform-origin: 407px 334.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 7.91667px; transform-origin: 14px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.icfpconference.org/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eICFP\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.65px 7.91667px; transform-origin: 146.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e held its annual 3-day contest in July 2021 with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eHole-In-Wall\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.95px 7.91667px; transform-origin: 29.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Contest \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/spec-v4.1.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpecification\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 237px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 118.5px; text-align: left; transform-origin: 384px 118.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.267px 7.91667px; transform-origin: 230.267px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe contest folds the figure in Red to fit within the hole shown in light grey \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 238px;height: 237px\" 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C2C2dob50oE//IZOXfxlS5iMjccu1/R4rL1sXtVKu0yV4KFf/YxOn2M9rnsBHfztr2lXkCd9ug7jujB/BbnJbJ2vNboI29AgL+rrqmcvFMBMbOmopd2uS+jwT35M9DluPDaA/Rz00o7YENr/l6fp5KXjxnUfvI/2LP+IBk2tE+5zADOxureJIkJ92bpfS3QRtmVFmexFApjOtvJcGn7/LTp6Gzce+zwNZaHHZKaG8lJo5PUX6dhNtuO6x77/XRp+5zXaVoz7FOamsiyHrfu1RPNhGxcdROvXtLMXCGAy29Niad8/n6Xj37zaJhjGxmML2M/B9LbWl/DjuldeTvv/8RfanhTJfg5gMpsGuikpPozNAK3QdNi6uSymehVe4g76sTPUlw78/gk69eWLLCFgOx6L5RjtZfOqFn5c94Lz6eBvfkW7Aj1p87pO9rMA4zWb/ojzcl/OZoEWaDpspWnh3EUBsCaNx+4x/WF2+JEHLRW+5ORXv4LxWJVMPq57L+1Z/iENNmNcF6aXnRHHZoEWaDZs/X1dqQMP1MMUtpXn0PD7b9LR226xqeAxHus4Y+O619tck2Pf/w4Nv/0qbSvKYD8HIOkx/eEcHODBZoLoNBu2Bbkp7MUA2J4aQ/te+PvE8dgf3k57//suba3CeKyjTTque8XltP/ZZ2hHYgT7OYCSwnQ2E0SnybCNDPOj/r4m9kKAQW3ooZ0hPnTwySfo1EVj47F05pl06NGHabf7ctrSjfFY0diO655tuW6nzj+PDj7xK9plasVsXtvBfhaMad3qNoqJDGSzQWSaDNuqshz2IoDxbGmvoT3Oi+nwww+MBazJyUu+Qgee/h3tjMB4rFZYxnW//n821/LwA/fQnmXSuG4F+zkwntqqAnJxWsTmg6g0F7bS9O+P13ezFwCMY5vpD67h996goz/4vk3FfPzb19K+l56jIbxRTLOGclNo5LV/0bEbx43rfu9mGnn7FYzrgiwtOZLNCFFpKmy9PJZTc0Mpe+LBGLanRtO+F/5GJ665yqYiPvrD22jvf9/BeKyObK0rob0L36cjd99pc61PXP4N2v/3P9OOhHD2c2AM7c0V5OftzGaFiDQVttkZ8exJB51b3007g73p4JOP06mLvjRW8VrGY5dhPFbHNq9sod2mSvXQLx+l02dbjeuedx4dfPyXtMvfnTbjxTaGlJ+TxGaFiDQTtsGBntTTWceecNCnwbZq2uO0iA4/NNl4rD/7OdCvHTHBtP+ZpyaM6x65/x7as/R/NNhUzn4O9GlVTyOFh/iwmSEazYRtaWE6e7JBf7aVZtPwv9+go7fy47HbM9HDYXRDucn8uO53b6KRt16hbagvDKPCVF9wmSEaTYRtbFQgDfS3sSca9GN7SjTte/6vdOLqK20q0LHx2Hz2c2BcW+uKJxnXvQzjugaxcV0nJcSGstkhEuHD1tV5EdVh0ot+re+mXcFedPB3j9GpL104VmHajMdi+USY2uaVzey47unzvkgHH/sF7fJzo839GNfVq0bTH12ebsvYDBGF8GGblhzFnlzQtsHWKtqzYiEdfuj+sYA1OXnJxRiPhXmRxnUPcOO6991Ne5b8lwYby9jPgbZlpceyGSIKocPWz8eF2rHwtK5sK8mi4Xdfp6O3fM+mIjz+rW/Svhefo+2YcQ52Mum47nduopE3X6ahgjT2c6BN3e01FOTvzmaJCIQO2/ycZPakgvZsT46i/c/9lU5cdYVNxXf0jtto+IN3aGslxmNBGWPjuj+0KXsnvnEZ7f/bn2hHfBj7OdCeYtMfUFyWiEDYsI0I9aFVvY3sCQWNGOiiXUFedPC3j9GpCy8Yq+jOOIMO/fRh2u22jLZ0YTwW1GE7rvsFS3k8/cVz6eBjP/9sXBcTMbVs7apWio4IYDPF0YQN28rSbPZkgvhGx2M/osM/vm8sYE1OfuViOvDUb2lnOMZjwbF2RJvHdb9mU0aP3Pcj2rv4AxpswLiuVtVU5psyZOGETHE0IcM2MS6UNplaRdyJBHFtK86k4Xdfo2O3fNemAhsdj/0HxmNBOEM5yTTy6j/p+A3X2ZTZYzffSCNvvERD+ans50BsKYkRbLY4knBh6+m+jJrqStgTCGLanhRJ+//xFzpx5fjx2B/Q8AdvYzwWhLe1tpj2fvQeHfnRuHHdyy6l/X/9I+0wNQC4z4GYWpvKydfLic0YRxEubLPS49iTB2LZvK6TdgV60sHf/JpOXWA7Hnv4pw/RbrelGI8Fzdnc10y7TZX0oV/8lE5/wWpc99xz6dCvf067fF1p8+pW9rMglrysRDZjHEWosA0K8KDujhr2xIEYBlsqac/yj+jwg5ONx/qxnwPQmh3RQXTgz3+gk/83blz3XvO4LlYgE9nK7gYKC/Zms8YRhApbado2d9LA8eTx2HdepWPf/45NxTM2HoseCdCnoZykScZ1b6CRN16koTyM64qqvCSLzRpHECZsYyIDaC26Z4SzIzGC9v/jGTpx5eU2Fc3YeGwe+zkAvdlaW8SO65689Ou0/y9P047YEPZz4Dgb1nZQfEwImzlqEyJsXVYspFpMohHGZlMB3RXgQQef+BWduuD8sYrFZjwWyx2CMW3pa+LHdc85hw796me0y8eFNq9qYT8L6msw/ZHk7rqEzR41CRG2qUmR7EkCdQ02V9CeZR/S4QfuHQtYE8t4bBjGYwGsTTque89dtHfRf2hrPZ6sEEFGagybPWpyeNj6ejtTW1MFe4JAHduKMmjk7Vfp2PfGjcdeew3t+9c/aDtmiANMadJx3ZtuoJHXpXHdFPZzoI6utmoK9HNjM0gtDg/bvOxE9uSA8qQXsUtjTdZLkkmk9xfv/fA9+fV23OcAgCe97lHqHZL+ULW+p6R77MAffktDWajvHKUoL5XNILU4NGzDQrzl6dnciQFl7f3fv20qA8nR22+lnSE+8juNuc8AwMxJryWVupPH32f7Xvgbuz0oa83KFooyXRMui9Tg0LCVpmVzJwWUd/yaqyw3/8lLvkJDmQnsdgAwP1IP0slLx9bWPfm1r7LbgfKqK3Ll7HFxeo+8PJ4gP7/vUmDAFRQcfJEsMPByCvC7nrw8f0Guzm9OyKz5cFjYJsSG0MZ1newJAWXt8ne33Phm0tgsty0AzI/0juXx95u04hW3LShr66c5lJ/3C1OwXkihoQumFBLyBfLzvZ3cXZ9lM2y2HBK2Hq5LqbG2mD0ZoDzpkQXphj9xzdWWN0GdPuss+a043PYAMDd7nBdbHp+T3jxlnkAlrYiFx4PUtX0wnk6e+D/asmUBxcfzAcuRQldqBXNZNhsOCdvMtFj2ZIDyrFu18qom2Ul09PYfyP+WXlyxM9SH/RwAzM6OmGA6/u1r5Xvr2Hdvou3JUTT8n7cs9x9at+rZtcOVTp8+m0wnXtbSwgfrVHy872PzbKZUD9tAP3d5GjZ3QkB55latVAls+2zMfFewF524/DL5/x/94W00lIvHFADmY1tpNh25/x75npLmREiL1kv/f2tdseURO7Ru1bF7hzOdPHmJJWgle/cuoMxMPlSn4u31CJtrM6F62BZhfUiHGd+qtf7Z3oXvE515pvyzg4//kgbxBxHAnEhvmJJeAmO+14bfe9Pm52jdqmfwk0o6dfIim6A1W7mSD9QphZxB7q5/Z7NtOqqGbVSEvzz9mjspoDybVq3pL+/xP9/3wt/ln0ukxQXG/xwApmc9IUpaC3fzWtuJoGjdqmf/yJ/YoJUcPbqASkqYQJ2GNFvZZcV/2IybiqphW12Bl9Y7ylStWjNp+TxpzU5pm9NfwIQpgNna47LEMiHq8E8eoq01Rex2w/9523I/onWrjK2bC4hOn8kGrdnGjQsoMpIP1al4uP+BzbipqBa2KYkR7AkBdUzXqjWznTB1Be0M9WW3AwBb0qo/x6/7lnzvmCdEcdtJ5NbtZ8tVonWrjOE9r7MBO15dHR+oU/HzvYXNuamoErY+nk7U2ljOnhBQ3kxatdZsJkzdeTve6wowjW1l2XTkgYkToqaC1q2yjh65lQ3X8bZvX0DJyXyoTiYk5BxTtn04IeumokrY5mbh7USONNNWrTWbCVNP/JK2tNew2wEY3ea+Zjrw1O/ke0UyfkLUZNC6VdbJk19lw5XT2cmH6lTcXF5i824yiodtaJAX9XXVsycDlDfbVq012wlTz7HbABjdyJsvW+4TbkLUVNC6VcbgJ9WmED1jQqhOZv/+BZSXx4fqZDzc/spm3mQUD9uy4kz2ZIA6LK3a674141atme2EqS/QniX/ZbcDMKrdrkvo1IUXyPfIVBOiJrO1rgStWwUMflrGhupU1qzhQ3Uy7iKFbVxMMK1f08GeDFDefFq1ZqMTpm6Vf4e09B4WkAcYtSM2lI5fP7MJUVMZ/gCtW3vb/HEznT59Lhuqkzl1agFVVPDBynF3/Qebe5NRLGzdXZZQwyz/ygP7mk+r1pr1hKkjd91BQ3gxCRjctrIcOvzAvfI9MdMJUZNB61YZ0nuQpRCdjc2bF1BsLB+u47k6vcVm32QUC9uM1Bj2BIA67NGqtWY7YepXmDAFhrV5ZTMdeHr2E6Kmgtat/R3Y/wQbqNNpbubD1VpgwJVs7k1FkbAN8HWlztYq9gSAOuzVqrVmM2HqJUyYAmMaeWvuE6Img9at/e3ZuZgN0+ns3r2AMjL4kDXz9b6Hzb6pKBK2hXgu06FsWrVvvsxuMxc2E6bO/gLtWfo/djsAvdrtupROXXihfA/MZULUVNC6ta+tm/Pp2FHTHzBMoE6nt5cPWUlw8Hnk4fYMm31TsXvYRob5UX9fM3vwoA4lWrVmNhOmrr6SdoZjwhQYw444aULUt+WyP58JUZPZWi+1br8r/360bu1j7+5/s2E6nSNHFlBRER+2vj53stk3HbuHbVV5LnvQoA6lWrXWMGEKjGabqV47/KB9JkRNBa1bO9vUZQrO29lAnc6GDQsoPNw2aIODLyIXp3fZ7JuOXcM2OSGcPl7fwx80qELJVq01mwlTv/k1bemoZbcD0DqphXngj0/KZV1ijwlRk0Hr1v6GBpPp6JHb2ECdTm2tVdAGfZk83J9is28m7Ba23h4rqKWhlD1YUIcarVprNhOmXn6e3QZA60beesVSzu01IWoqaN3a3/atkXT40INsoE5l27YFlJQkzT6+nDzdn2Szb6bsFrY5mfHsQYJ6bFq1Zcq1as1sJ0ydjQlToDu73ZbSqS9ZT4gqZLezJ7RulSG96GL/vqenXXZvvIb622f9TC3HLmEbEuhJvZ117AGCOtRu1ZrZTpi6inaG+7PbAWjNjvgwOn7DdXLZVmJC1FSGP3jHcj+jdWtf27Zk0qEDP6PTp77IhqvMFMhHDt9FO7aF0qreRooI9WGzbzbsEralRRnsQYF6bFu1Oew2SrGZMPWjH9JQQRq7HYBWyBOiTK1KqUwrOSFqMnLr9ha0bpW0eVObHKZ7di6ikb0vyvbs+pB2bveRW8HW21aWZrPZNxvzDtvYqCAa6G+32TFQl6NatdZsJkz9FhOmQLs2r2pVbULUVNC6FcemgS5KjAtlM3Cm5hW2rs6Lqa5a+TEMmJqlVXu9+q1aa7YTpl5gtwEQ3cjbr1rKsRoToiaD1q1YmupKyNN9GZuFMzGvsE1PUW8MA3gitGrNbCZMnXMO7Vn2IbsdgKh2myrTUxd9aTTgVJoQNRW0bsWSlR7HZuFMzDls/X1cqMNUuXI7BOoZa9V+26GtWjObCVPXXEU7IzBhCrTBkROiJrO1vhStW4F0d9RQUIAHm4nTmXPYFuQmszsD6hGpVWvNZsLU3dKEqXR2OwBRbK3IM4XZ/XKZdcSEqKns/S9atyIpLkhjM3E6cwrbiFBfWt3bxO4IqEe0Vq012wlTj9EWPBoGgtq8upUO/On3lkBz1ISoyQyaWrdH0boVxlpTeYmJDGCzcSpzCttKwSp2I7Jp1b4lTqvWmvWEqZFXMGEKxDQsyISoqaB1K5baynxyWbGQzcfJzDpsE+PC5GnQ3A6AekRu1ZrZTJg69xzas/wjdjsAR9ntvpxOffkiuYyKMCFqMqOt2++N7idat0JITYpkM3IyswpbL/dl1FRfwn4xqEcLrVoz6wlTx795Ne2MCGC3A1DbjoRwOnbj9XLZFGVC1FTQuhVLW1MF+Xo7s1nJmVXYZmfEsV8K6tJCq9bariDrCVN30rZCTJgCx9pamUeHHxJzQtRkBhvQuhVNnqkxwWUlZ8ZhGxzgQT14K5DD2bZqX2G3EZHNhKnfPUZbuurZ7QCUtnl1Gx348x8s95FoE6KmgtatWFb2NFBYiDebmePNOGzL8P5jIWitVWvNZsLUq/9ktwFQ2vA7r1nKoagToiaD1q14pGzkMnO8GYdtW3MF+0WgHq22as1sJ0ydiwlToLrdHtYTon4s7ISoqaB161ir+5rk1xRnZ8TLj8G6Oi9iM3M8hK2G2LRqy7X5+NWECVORmDAF6tiRGEHHbtLOhKjJoHWrrvVr2qnFdM4Lc1MoNjqIvEx/sHEZOR2ErUZovVVrzWbC1D130TYMUYDCtlbm0+GHHpDLnFYmRE1l73/ftdQHaN3a1ycbeqiztYrKijMpOSGcAnxd2UycLYStRti2anPZbbTEZsLUk49jwhQoZnO/didETUZu3d6K1q299Jnqn+qKPMpIjaFQU2OAy8D5QthqgJ5atdYwYQrUMPyudidErfx4FVVtXkup2zbIajevof6PV8o/Q+t27taY/jhpqC2i3KxEiorwJ3fXJWzu2RPCVgP01qo1s5kw9cUv0p4VC9ntAOZqt+cKOnXxl+UyppUJUVLA/m/3NrrjyEH6/OnTZIpTG2eb/t+9hw9QQE8bHUHrdkY2ruuktqZyKs5Po4TYEPL1cmJzTkkIW8HptVVrZjNh6tpraGdUILsdwGyNToi6QS5bWpkQ5bRrkC4+eWJCwE5mibub6T9M/2WC1q2t7vYaqijNll+rGGSqR7lcUxPCVnCWVu0N1+mqVWvNZsLUvZgwBfO3taqADj+snQlRUvfwn/ftZgN1Klds3kzNd91l+ofpj/GH7jd063ZVTyPVVuXLC7yHh/iQi9PsFgpQGsJWYHpv1VqznTD1BG3pbmC3A5jO5jXtdOCZpyz3jugToqQx2FuPHmLDdCbe9vQ0/Yfpv0x2uhundbuuv01+V39+TjLFRAWSp+nYuewSBcJWYEZo1VqzmTD12r/YbQCmM/zu65ZyJPqEqDWmoH1mDi1aa1LrtulHPzL9YwGt/Okjum3dfry+mzpaKqm0MIOS4sPI38eFzSpRIWwFZdOqfVvfrVozmwlT532R9jhhwhTMjjQh6qSGJkRJY7Tjw3Mu3vLyMv2H6b9MGn3c2e/Sot7OOqoqz6H0lGgKCfRks0krELaCMlqr1mwoO3FswtS3vkk7o4LY7QDG254UScduvlEuO1qYEFW+ZR195+hhNjxn6/ItWyyt2+afPUrdazrY7xRdf18z1Zv+QMrJTKDIMD9yc1nM5pEWIWwFZMRWrTXbCVM/om3Fmex2AGbyhKhHHpTLjFbeECU93jM+NOfDunVb5evBfqdoNqztoJbGMirMS6W46GDy9lzB5o8eIGwFZNRWrTXrCVMHfv8EbenBhCngbTa14vZraEKU2UOH9rGhOVfWrduuR38i7NhtV1s1lZv+gE5JjKBAPzc2b/QIYSsY21btq+w2RmEzYer1F9ltAIb//YalnGjlDVHSiyu4F1bMl3XrVpTnbld2N1BNZR5lpsVSWPDM1n7VI4StYNCqHWM9YerUeefRHqdF7HZgXLu9nOjkVy6Wy4iWlswrHBxgw3K+rFu3+37smOdu165qpca6YsrLTqLoiADycFvKZorRIGwFglbtROMnTO2IxoQpGCVPiPqOdiZEWUvctpENS3tQu3W7aaCL2k35UFwgvQoxlHy9ndkMMTqErUBsWrUVxm7VWrOZMHXf3bStJIvdDoxja3UhHX7kx3KZ0OKSeXHbNrFBaQ/WrVul3pnc01FLlaXZlGb6Ayc4wIPNDLCFsBUEWrVTs50w9Rva0tPIbgf6t3ltB+3/y9OW+0WLS+aVbFnHBqW9vGvn1u3q3iaqqy6g7Ix4igj1JVenRWxOwOQQtoKwbdXmsdsYHSZMgWT4Pe1NiBpPekWjtHqPORzt7QeffExHf/B90z/m1rod6G+n5oZSKshNptioIPLyWM7mAswcwlYAaNXOjM2EqfPPoz3OmDBlNLu9nOVuYzlENDQhivPzgyNsUNrD3/btpr3/+7fpH6Z/mUzXuv1kQw91tlZRaZH0KsRw8vd1ZXMA5g5hKwBzq/bYjdfRVrRqp2QzYerb19KO6GB2O9AfaQLUse/cNHqvaGxCFMder2rkxA1tosHGsilbt31d9VRdnksZqTEUGuTF1vtgPwhbB7Nu1Q6jVTsjmDBlPFILVmrJStdcixOiOI2frqEfHjnIhuV8/MzUYpYWOJC+w7p1u235R9RQW0S5WQkUFe5P7i5L2LoelIGwdTC0amdGWnJvKCeZdvm6yl3t5r/YhXTmmbTvpefY49CC4fffpNOf/zx/bAI49r2b5TIglQWpTGh5Ocbg7Z+wgTlX0osycgbXy797w9pO6s5NpuEbrjP9cAF9fOP15LHoP2z9DspD2DoQWrW2xgfqwcd/SUdv+R6d+vJFlvOkFSe/egl7jFpw8rJL2WMSmVRGpLIilRmtBfELIzvZ4JyLl9avpoqSLEpNiqRAU/0i1d0Vn/1BLyn43WMT6nZQB8LWgcZatdcbplVrl0A1tRyPX3uNzPz/Rt54UQjHr71a3h+p5c0dvxYceeAe+RikrnruGB3BfJ1PXHXF6HX/7DGwmRA9iDdu6qO7jhxgw3NaIyO0YP16WtDYSLelJJLLioUT6u6A99+kwSsvN228gDZc/220bh0EYesgem7VDjaU0vaUaNrtsYJG3npFfi72yN0/pBPSDX/GGZbjnsqpCy+gYzddL4/T7X/2Gdr74Xu0M8SHhgrSLJWk9P/M24/fB0cxjyseufN29udaIOIxmK+zFLzSv7f0NtG2wnTaGeYrP4O9/7m/0KFHH5aX2Dt10Zcs20/nxOXfoCN33UEHf/e46Xe/RLvdl8lvptpaVzxhH5TU8clqenF4J5013eNAhw/Tgk8/pQXt7bSgsJAWxMTQF0OC6RFvd1o0xbOvaN06HsLWQbTeqrUEqqeygToVhK0ytBC2U5kQxP+YQxB/7nNjQfzk+CAuYb/XHnx2bKb7D+8fC9eTJ2nB0BAt6O2lBeXltCApiRaEhlrc7OdDf3F3Yutsa2jdOh7C1gFsWrXviNuq5QP1ztkHqukPitFA/fOsA3UqCFtlaD1sp2KXFvFkQZwcZZcg7uyqp0UNlXRfSQGdn5ZqE66SLwUH0R2+XvSs++zWfq34JVq3joSwdQCRWrWTB+oVRGc6PlCngrBVhp7DdirKtYiXTxnE/X3NVF9dSDmZ8RQZ5kduzott6t5lKxbSe85LZCuYMdmZQuvWsRC2KrNt1b7GbmNvgw1ltD3VKlD/YB2oM5to4qhAnQrCVhlGDdup2C2Ir/gGHTad152/fJQG/vR7anj+b5T28vMU+O/X2XrX3tC6dRyErcqUatWOBmrMxEC9apaBahlDFSNQp4KwVQbCdnbsEcSnTUE8/OWL6JNvXk29t91CdQ8/QPmmlnHC83+1axCPtm5NdYLpO9G6VRfCVkXzbdWOBaoTjbw9j0C1tFBnPylJJAhbZSBs52+l6V6qMf0xnRsbTBkf/psynnmKyn/1KLXecxetu/kG2n7Z1+nIuedajmsqkwbxC3+bUxCjdesYCFsV2bRqK/lWrfQ+07FAfdUOgSp+C3WuELbKQNjO3tpVrdRYW0x52YkUHRFAHq5L2XrUmtfC9yjytX9ZgrhtrkF88eyCGK1bx0DYqsS6Vbvvn8+OC9Tf0pF7EKizhbBVBsJ2ehvXdcl1YrHpfkuIDSFfL2e23pwr+wXxl9kgbnjofst2aN2qA2GrkhPf+OwVeDMMU5lpW+ltOYdNN4YcqIs/oB3RQbS1qoD9DqNB2CoDYcvr7qilitJs+VWIQQEebD2plpC3X6HUv/+Jyn79M2q7+05ab2qh7v7qJXRqho/kSczbHrzgfLRuVYCwVcFgfcmEgm6BQJ0zhK0yELajVvc2UZ3pPszOiKOIUF9yneINTSKZSxAnm+oe7neB/SBsVbC1tthSqKVQRaDaB8JWGUYN24H+dmquL6WC3GSKjQokL/flbF2oZdZBvPbmGyznNfLVf7Lbg/0gbFVgHbbSuCq3DcwewlYZRgnbj9d3U0drFZUWZVBSfBj5+7iydZ9eJT7/V8t5RdgqD2GrAoStMhC2ytBz2PZ11VNVeS6lp0RTSJAXW9cZBcJWXQhbFSBslYGwVYaewnbNyhZqqCmi3KwEigr3I3eXJWz9ZkQIW3UhbFWAsFUGwlYZWg7bDWs7qLWxnIryUyk+Jph8PKdfEceoELbqQtiqAGGrDIStMrQWtl3tNVRekkUpiREU6OfO1l8wEcJWXQhbFSBslYGwVYboYbuqp5FqK/MpMy2WwkK8TfXT3FfCMTKErboQtipA2CoDYasM0Y5h3epWy3XufvwX5Om2jK2jYHYQtupC2KoAYasMhK0yHH0Mmwa6qL25kkoK0ykxLpT8vF0s17n+oQfY+glmD2GrLoStChC2ykDYKsMRx9DTWUeVZTmUlhxFwcyrEM3XGWFrPwhbdSFsVYCwVQbCVhlqHEN/XxPVVxdSTkY8RYT5kqvzYrbeMTNfZ4St/SBs1YWwVQHCVhkIW2UocQzr17RTS0MZFealUFx0EHl7rGDrmcmYrzPC1n4QtupC2KoAYasMhK0y7HEMn2zooc7WaiorzqTkhHAK8J3fqxDN1xlhaz8IW3UhbFWAsFUGwlYZcz2Gvu56qq7Io4zUGAq186sQzdcZYWs/CFt1IWxVgLBVBsJWGTM9hrWrWqjRVLbzshIpKsKf3F2VexWi+TojbO0HYasuhK0KELbKQNgqY7Jj2Liuk9qaKqi4II0SYkPI10u9VyGarzPC1n4QtupC2KoAYasMhK0yrI+hu72GKkqzKTUpkoL8HfcqRPN1RtjaD8JWXQhbFSBslYGwtb9VvY20+5675GPYdt23yMVpEVsfqM18nRG29oOwVRfCVgUIW2UgbOdvoL+NmutLqSAnmWKjAsnTfRmtu+n60XN6zVVsXeAI5uuMsLUfhK26ELYqQNgqA2E7ex+v76aOlkoqLcqgpPgw8vdxmXCvI2yNAWGrLoStChC2ykDYzkxvZx1VledSeko0hQR6sve3NYStMSBs1YWwVQHCVhkIW17/ymaqryminMwEigz3IzeXqV+FOB7C1hgQtupC2KoAYasM67DdnhQphKO33yrvj5phu2FtB7U2llFRXirFxwSTj+fsXoU4njlst1/6f3KFLALzdUbY2o/1eUXYKg9hqwKErTL2PTdWWYjm1AXns/tsL11t1VRekkUpiREU6OfG3rNzdfD889ljEkHfD77P7jPMHsJWXQhbFSBslbHHeZHlvArnzDPZfbYXJcP2xFln8cckgKqfPcLuM8wewlZdCFsVIGyVsz01hnbEhLBduo4w8vLzlmst/ZvbZ3uz7kaOiwkm73l0I0db7X/bPXdaunEdLeXZP1Psv55l9xnmRjqv5muNsFUewlYFCFvj2FaaTafPOUe+1sP/fYfdRmn9fdIEqcLRCVJhs5sgVfzELy1lNealf7DbgD4gbNWFsFUBwtZYjt7xA/laH/r1z9mfq2300Z+cGT360/3ZvkuTo1yW/Y/dBvQBYasuhK0KELbGsv/ZZ+RrfeKaq2hLXxO7jaNYXmpRmC6/1MJv3Esthi67VN73nttvsfn/oD8IW3UhbFWAsDWW3Z4rLNd7h0rjtnO1bnUbNdWXUH5OEuV/9L5lv0se+zlbD4B+IGzVhbBVAcLWWGzGbT9wzLjtXOxZPvbyiGrnRRRuKqsuKxay9QFoH8JWXQhbFSBsjUe0cduZOPD07+R9Pnbj9fTpQJf8/+Ql9kqy5CX2Ah24xB7YH8JWXQhbFSBsjUfkcdvJHPvOjfI+H/jDb9ifb1jbSa1N5VSUL72pKoR8VFw8HuwPYasuhK0KELbGYzNumxjBbiOSoZxky/7uWfo/dpvx1qxsoYaaIsrNSqCocH9yd1nC1h0gJoStuhC2KkDYGo/tuO3b7DYisR6vHcpKZLeZTl9XPVWbVxcK8mLrERAHwlZdCFsVIGyNSUvjttx47XzIjxi1Vlmtm+vK1ivgOAhbdSFsVYCwNSbLuO3VV9GWXoHHbTf0TDteO18D/W3UXF9KBbnJFBsVSF7uy9l6BtSDsFUXwlYFCFtj0sq47VzGa+drdW8j1VUVUHZ6HIWH+pCL0yK23gHlIGzVhbBVAcLWmLQybmuP8dr56u6opQrT+ZIeMQrCI0aqQNiqC2GrAoStcY2N2/6M/bkI7D1eO18b13VSW1MFFRekUUJsCPniESNFIGzVhbBVAcLWuIQft5XGa29Wdrx2vtauaqFG0z2UZ2p1R0X4k7srHjGyB4StuhC2KkDYGpfo47ZDOUmW/VNrvHa++rrrqboijzJSYygUjxjNGcJWXQhbFSBsjUv0cds9yz+0lE1HjdfOxyemlnlnaxWVFWdSckI4BfjiEaOZQtiqC2GrAoStsVnGbX8l3rjtgafEGq+dr/Vr2qmloZQKc1MoNjqIvDzwiNFkELbqQtiqAGFrbGPjtlfSlt5GdhuH0MB47Xyt7muiuuoCys6Ip4hQX3J1xiNGZghbdSFsVYCwNTZRx221OF47Xz0dtVRZlk1pyVEUHODB1nVGgbBVF8JWBQhbY7MZt/2POOO2e5Zpe7x2vjYNdFG7qV4rKUijxLhQ8vV2Zus+vULYqgthqwKELYg4bnvgqd/K+6SX8dr5WruqlRrriikvO4miIwLIw20pWxfqBcJWXQhbFSBsQbhxWwOM187Xyu4GqqnMo8y0WAoL9mbrRS1D2KoLYasChC3YjNsmhLPbqGnI1Hoz749Rxmvnq6utmsqLMyklMYIC/NzYelJLELbqQtiqAGELoo3bGn28dr7Wr+mglsYyKsxLobjoYPI2/THF1ZsiQ9iqC2GrAoQtSEQat8V4rX319zVTfXUh5WTGU2SYH7k5L2brUZEgbNWFsFUBwhYkNuO2PQ4ct13fTcduvkHeF4zXKqO3s46qynIoPSWKggM92TrV0RC26kLYqgBhCxJRxm0xXquuTQPd1N5SSSWF6fIjRn4+LmwdqzaErboQtipA2ILEdtz2LXYbNWC81rHWrW6jproSys9JopjIAPJ0W8bWuUpD2KoLYasChC2YiTBui/FasazqaaTaynzKSoulcFP94Lxi4YT6VwkIW3UhbFWAsAUzy7jtVQ4at5XGa2/CeK3IutprqLwkS37EKNDPna2P7QFhqy6ErQoQtmDm6HHboexEy/djvFZ8G9Z2UGtjORXlp1J8TDD5eDqx9fNcIGzVhbBVAcIWzBw9bovxWm1bs7KZGmqKKDczgaLC/cjNZQlbX88EwlZdCFsVIGzBmmXc9pePsj9X0oE/YLxWT3q76qiqPJfSU6IpZJaPGCFs1YWwVQHCFqyNjdteoe64LcZrde1j0/XtaKmk0qIMSooPI/9pHjFC2KoLYasChC1Yc9S4LcZrjWWgv42a60upICeZYqMCydPd9hEjhK26ELYqQNiCNZtx2/fVG7eVAtZcDjFeazyrehuptqqAstLj5EeMkp7/m6U8IGyVh7BVAcIWxnPEuK1lvPYmjNdCL6031UXmeinN9EcfV++D/SBsVYCwhfFsx20b2G3sCuO1MM72pEhLvbQlJ5namsqpOD+NEmJDyMfLfo8YwSiErQoQtjCezbhtfBi7jT1J3cbm78N4LUisw3aoIM3mZ2tWtVBDbRHlmspNVLg/ubvO/REjGIWwVQHCFsZTe9wW47Uw3lRhO15fVz1VV+RSRmoMhQZ5sRkBU0PYqgBhCxw1x22lrmPpuzBeC2azCVtrn2zooc7WKioryqDkhHDy93VlMwNsIWxVgLAFjs24bbeC47YD0njt9fJ3YbwWzOYatuMN9LdTc0MpFeRKjxgFkZfHcjZDjA5hqwKELXDUGrfFeC1w7BW2463ubaK66gLKzoijiFBfcnVaxGaK0SBsVYCwBY7tuO2b7Db2gPFa4CgVtuP1dNRSpamspyVHUXCAB5svRoCwVYFewnaL6abZERUo36RKkVt4BhpTNI/bHv3hbez5sIfD998jf4eh3odsOs4dMSHs+bCXHVFBtKW1iv9+DZCOwVwvKRm21jau65KzpNj0fQmxoeTr7czmjR4hbFWgh7DdWlVAdMbnLMehpOPf+ia7D3p09PZb2XOghGPfuZHdBz06+oPvs+fA7j73ORrKS2H3QXSOCNvx1q5qpUZT/ZiXnUjREQHk4bqUzR89QNiqQA9he8TU8jIfg+LOPJM2r2xm90Nvjptam+w5UIA0EYvbB73Z3N9GdNZZ7DlQwrHvfUeTPQYihO14K7sbqKYijzLTYigs2JvNIq1C2KpA62G798P3LPt/8De/tnSj2dvw269avmfP8o/YfdGTrXXFdOLyy0bP689/wp4Tezj428fk7zj15YtoW3Emuy96stvLyVKO9r3yPHtO7OHAU6Ovv5QMv/s6uy8ik47BvP+ihK01+RGjtmoqM5VZ6RGjAD83Npu0AmGrAi2H7fbUaLlbV9r3ww/cS4MNpex29iA9/iKNK0rfdejXP2e30ZPdbsvGykW4P7uNPVhXqnsXf8BuoyfmEJRa8oONZew29iDNYTj0s0dGv8v0R5M0RsxtJyrRw3a89WvaqaWhjArzUiguOoi8PVawWSUqhK0KtBq2m1e30sEnfiXv98mvXEw7g73Z7exp/7N/Hv2+r11CWyvy2G304uDvRlucx757k+Ld5kfvvF3+rkOmFjT3c70YbCqnE1dfKR+rtPACt4097YgJphPfGO2dkIJXCmBuOxFpLWzH6+9rovrqQsrJiKfIMF9ydV7MZpcoELYq0GrYWncfj7zyAruNvUnnx/yde1YsZLfRA+su5H3P/43dxp5G3nhR/i69dyXv9na2lB+pO5nbxt6G33nN8p1a6k7WetiO19NZR5VlOaOPGAWK94gRwlYFWgxb6+7jI/ffQ4P1ynUfW7PuSj74mH67ktXqQjYzSlfygad/Jx+j0l3I1uTu5EcfHv1eDXUn6y1srW0a6KL25koqKUynxLhQ8hPgESOErQq0FrbW3cenLv4y7VKh+9jaWFfyV2lrZT67jdap2YVspveu5EFTHXXimqvkY1SjC9najuggOnHZpaPnVyPdyXoO2/HWmeq0proSys9OopjIAPI0/bHL5ZySELYq0FrYWncf73tZne5jazZdyU7660pWuwvZTO9dybt8XCzlRq0uZGvD74zNptdCd7KRwna8lT0NVGP6Qz4zLfazR4wWTsg8e0PYqkBLYWvbfXw3ba0vYbdTkm1X8i/YbbRM7S5kM713JR/445PysanZhWxtS3sNHfrpQ6P7oIHuZCOH7XhdbdVUXpJFKYkRFKjQI0YIWxVoJWxtuo9NrZ9dQV7sdmqwdCX/39doa5W+upId0YVspteu5MHmSjr+zavlY1O7C9ma9ArHk5d9ffQcC96djLDlbVjbQa2mP9aK8lIpPiaYfDzt84gRwlYFWglb2+7j59lt1GLTley8iN1GixzVhWym167kXT6ulvLiiC5kayNWL2cRuTsZYTsz/aY/iOtrCiknM4Eiw/zIzWVujxghbFWghbC16T6+7245FLjt1GLTlfz4L9lttMhRXchmeu1KPvDH38vH5KguZGuDbdV0+CfW3cnB7HaOhrCdm97OOqoqz6H0lGgKCfRk85Iz47CtKM1mvximJ3rYTug+NhUgbju1WbqSv/5/8kII3DZa48guZLMjOutKHmyppOPXXiMfkyO7kK3tjAqkk5eK3Z2MsLUPaQUjLjPHm3HYhgZ5UV9XPftlMDXRw9am+/il59htHMG2K3kxu42WOLoL2UxvXcm7fMXpQrY28tYrlv0SsTsZYTt/q/uaKCLMl83M8WYctpLcrAT2C2FqIoetTffxvT+S95XbzhFsupJNLW9uGy1xdBeymd66kg/8SZwuZGuj3ck/Ht03AWcnI2znryA3mc1KzqzCVpqVJc3S4r4UJidq2Np0H1/0JWG6j61ZupIv/TptrS5kt9EKEbqQzfTSlTzYWiVcF7K1nZGB8jCIfK4F605G2M5PR0sV+fu4slnJmVXYSqSljqSlj7gvB56oYWvTffyiON3H1my6kl2WsNtogVQGROhCNtNLV/IuPzdL+RCpC9nayFsvW/ZRpO5khO38SBOkuIyczKzDVlKt89VY7E3EsJ3YfVzEbudoNl3Jv/k1u40WiNKFbKaXruQDf/6DfAyidSFbk1rfhx95cHQ/BepORtjOnbTakNssVxmaU9hGmSqLNStb2J2AiUQLW5vu4y9dSLsCPNjtRGHuSj5x2ddpa42YfxRMR6QuZDOtdyVLY6LmPxhF7EK2tjMigE5+/Wuj51uQ7mSE7dxI6+pK6+ly2TiVOYWtpCg/ld0RmEi0sN37kXX38T/YbURi3ZW823Upu43IROtCNht54yV5n7TalbzL332sXAjahWxt5E2xupMRtnNTWpTBZuJ05hy20vsjpfdJcjsDtkQKW5vu43vuMrUUxZ90ZNOV/NvH2G1EZtOFHOH4LmQzrXcl73/mKXnfRe5CtiY9D3z4YXG6kxG2s9fbVUchQTN/kYW1OYetJDMtht0hsCVK2E7oPja1DLjtRLT/2Wfk/T7xjUtN51NbXckidiGbabUrWXrp//FvXyvvu+hdyNakP7ak933L51zqTu50XHcywnb2pFc2clk4E/MKW3fXpdRgChJup2CMKGFrM/v4X8+y24jKpivZTTtdyaJ2IZtptStZmmdgKQ8a6EK2Zj7nEkd2JyNsZ6eloYy8Pea+KMG8wlYSHxNCG9Z2sjsHo0QI2+2pMWPdx3ffqblnVm26kk0tRW4bEYnahWym1a7k/X95Wt5nrXQhW5NWKDr88AOj++/A7mSE7cxJj7tKj71yGThT8w5bibQOILeDMMrRYWvTfXzhBZrqPrZm6Uo2VVCOXihhpkTuQjbTWleyNJP3+HXfkvdZS13I1qTHv05+7auj591B3ckI25mrLs9ls2827BK20kr3K00tD24nwfFha9N9/E9tdR9bs+lKdl/GbiMS0buQzbTWlSy96cxSDjTWhWzN/GIRiSO6kxG2M7PG9EdyVLgfm32zYZewleRlJ7I7Co4N24ndx9pdPcemK/nJx9ltRCJ6F7KZ1rqS9//1j/K+arEL2dpgcwUdfuj+0WNxQHcywnZmCvNS2cybLbuFra/pL8y2pnJ2Z43OUWFr0318wQXyq+247bTE0pV8xTdoa10Ju40otNCFbKaVruQtnXV0/Ppvy/uq1S5kazvD/Ojk1y4ZPfcqdycjbKfX2VZNAaZ6k8u82bJb2EpSTReP22Gjc1TY2nYf/53dRmtsu5KXs9uIQCtdyGZa6UreFeQ1dv013IVsbeR1x3QnI2ynl5Eaw2bdXNg1bJ1XLKSaynx2p43MEWFr0338ox/qZvF1267kJ9htRKCVLmQzrXQl7//bn+R91HoXsrXBpnI6/GP1u5MRtlNrqCkid9clTM7NjZ3D9iOKjgigtata2Z03KrXD1rb7+Hx5cW1uO60a60q+nAbrS9ltHG2sC/lm4buQzSxdyT97hP25o23pqqPjN1wn76MeupCt7QzzpZNfVbc7GWE7uQ1rOyg+JpjNuLmye9hKinHhbKgdtjbdxy+I34U5WzZdyR4r2G0cSWtdyGaidyXvCtZfF7K1kdf+ZTk+NbqTEbaTKzeVfy7b5kORsA3yd6fu9hr2IIxIzbC1effxXXfQVh1268tdyTeNdiUf+P1v2G0cSWtdyGaidyXv/7v+upCtDTZK3cn3jR6jCt3JCFten6l+CQ32ZrNtPhQJW0lWeix7IEakVtjadB+ff57uuo+tWbqSrzRVvA1idSVrsQvZTNSu5C1d9XTsRn12IVvbGepLJy/5iuUaKNmdjLDl5WYlspk2X4qFrafpr/smwR/NUItaYWvTfayh7su5sOlK9hSnK1mrXchmonYl7zS1NCzXW4ddyNZGXlWnOxlhO1FrUzn5mMoXl2nzpVjYShLjQmnjQBd7UEaiRthO6D6uyGO304vRWcmjLZ1jN98gv41HBId/8uOxa62hLmQz6wr4yIP3ssfoCEdv+a68T3rtQrYmHd/hB5XvTkbYTpSSGMFmmT0oGraSitJs9qCMRI2wlVpR5u+QbiJuG705cu/dlmMWzelzz2X3WQuk92dzxySCo7fdwu6z3kj1xMmvXCwfs/S4E7fNfCFsbdWYGihchtmL4mEbbio0q3oa2YMzCjXCdkd0kPxX//AHb7M/1yOpsjh91lmWcyuMz32ODvz5D+w+a8HIKy8QnXEGf2wOdPqsz9POyAB2n/Voz7IP5Xtasd4whK3F2lUtFB3hz2aYvSgetpL8nCT2AI1CrTFbAICZQtiOKc5PY7PLnlQJWz9vF2pvrmAP0ggQtgAgGoTtqK72Ggr0d2ezy55UCVtJWnIUe6BGgLAFANEgbEdlpsWymWVvqoWtq9MiqtPJ+3lnC2ELAKJB2PZSY10xebgtZTPL3lQLW0lMVCCt629jD1rPELYAIBqjh+3GdZ2UEBvCZpUSVA1bSUlhOnvgeoawBQDRGD1sK0qy2IxSiuphGxzgQT0d6i2QLAKELQCIxshhKz2OKj2WymWUUlQPW0l2Rjx7AvQKYQsAojFy2OZlJ7HZpCSHhK2X+3JqFnQdUiUgbAFANEYN27bmCvL1dmazSUkOCVtJUnwYfby+mz0ZeoOwBQDRGDVsU03HzWWS0hwWtpKqshz2ZOgNwhYARGPEsK2tyicXp4VsHinNoWEbEeZLq/ua2JOiJwhbABCN0cJ23epWiokMZLNIDQ4NW0lBbjJ7YvQEYQsAojFa2JYUpLMZpBaHh62/jyt1tFSxJ0cvELYAIBojha30uKn02CmXQWpxeNhK0lOi2ROkFwhbABCNkcI2Kz2OzR41CRG2bs6Lqb66kD1JeoCwBQDRGCVsm+pLyNN9GZs9ahIibCVx0UG0fk07e7K0DmELAKIxQthuGuiixLhQNnPUJkzYSsqKMtgTpnUIWwAQjRHCtrIsh80aRxAqbEOCvKi3q449aVqGsAUA0eg9bFf3NlFEqC+bNY4gVNhKcjIT2BOnZQhbABCN3sO2ICeZzRhHES5svT1XUEtDGXvytAphCwCi0XPYdrRUkr+PC5sxjiJc2EqSE8Lpkw097EnUIoQtAIhGz2GblhzFZosjCRm2kuryXPYkapF12AIAiEZPYVtXXUCuzovZXHEkYcM2KtyP1qxsZk+m1mwrymALOACACLanxbJ1l9YM9LdTbFQQmymOJmzYSgrzUtkTqjXWLdv9f/sT7XZbphl7P3qPTn7tqzY3puTUBefT8LtvsJ8xsmM3XCefnxNXX8n+XAuO3zh6DMevuoL9uZENv/u6XPat7wXJya9dYrpX3mc/I6p9L/7Dsv96admWmho2XJaIQOiwDfBzo862avakaolWx2yHMhPo8AP3WPZdujlH3n6VTp99tvzvo7d8j3ZEB7GfNarDP/mxfG6O3Hk7+3Mt0MMxKEEa45TOiXw/fO5zNPLGSzLpv+Xzddcd8jbcZ0WktzHb3s46Cgn0ZLNEBEKHrSQjNYY9sVqixbDlgnZz/+gbvobfe4NOn4PA5SBs9YkLWvPPtBq4egvbnMx4NkNEIXzYursuoYaaIvbkaoXWwnYoSwraey37vO/F52jzuFdpDr/3JgKXgbDVn6mC1mxC4CZHTdhGNHoK2+aGUvL2WM5miCiED1tJfEwwbVjbwZ5kLdBS2M4kaM1GA/cceTsE7iiErb7MJGjNtBa4egnbj9d3U1J8GJsdItFE2ErKizPZE60FWgnboaxE26B9afKgNUPg2kLY6seEoH1z8qA1G3nz5bHA/ZHYgauXsK0qz2UzQzSaCduwYG/q625gT7botBC2ctA+OLugNRt+H4FrhrDVh4lB+zK7Hcc2cH8obODqIWz7+5opMsyPzQzRaCZsJbmmQOBOuOhED1s+aGfXbS8H7rkIXISt9tkE7RlnzCpozeTANX1WPo+CBq4ewrYwL4XNChFpKmx9vJyotamcPekiEzlsh7KloL3Psn9y0M5xfHz4/bcMH7gIW22zR9CaTQjclGh2O0fReth2tlZRgK8rmxUi0lTYSlISI9gTLzJRw3Zi0D4/56A1M3rgImy1y55BayZy4Go9bDNSo9mMEJXmwlZSU5nHnnxRiRi2E4L25fkHrdlo4J4r/16jBS7CVpuUCFqzkbesAvducQJXy2FbX1NEbi5L2HwQlSbDNjoigNauamEvgohEC9uh7CQ6/GNlgtZs+D/GDFyErfZMCFpTOHLbzcfIW69YBe6dQgSuVsN2/ZoOiosOZrNBZJoMW0lxvnYKh0hhywdtJ7vtfBkxcBG22jIxaF9ht7MH0QJXq2FbVpzJZoLoNBu2Qf7u1NVew14M0YgStmoGrZkcuF80TuAibLXDJmjPPFPRoDWTA9f0XfL5lQI31XGBq8Ww7euqp9AgLzYTRKfZsJVkamRZKBHCdihHCtr7Lfux7+UXaPM6ZYPWbPg/bxsmcBG22uCIoDWbGLiOef+7FsM2NyuBzQIt0HTYergtpca6YvaiiMTRYevIoDUzSuAibMXnyKA1EyFwtRa2rY1l5OPpxGaBFmg6bCUJsSG0UeXgmC1Hhq0ctA9ZBe0r6get2fAHUuB+Ud4PvQaukcK2dvMa8ty5md7cu52e3r+H/jmyk/63exvFDW2igU197GccTYSgNZOWq7QE7j13qR64WgrbT0ykxz65DNAKzYetpKI0m71AonBU2A7lJNsE7YgDg9ZM74Gr97DdaApR151b6NrjR8lUqiZ13qlT9OsDw3Igj/8djjIhaE1hx22nJkcGrpbCtroij637tUQXYRtuCrBVPY3sRRKBI8KWC9pP13Wx26pNz4Gr57At3jJANx07zIbrZM4+fZpeG94hh7T171KbTdB+XoygNZMD17RP8jmXAjdNncDVStiuWdlCUeH+bN2vJboIW0l+dhJ7oUSgdtgO5UpB+4DlO+WgHRAjaM2GP3iHTp+nv8DVa9i6mFqz35ymNTuV3xzYS4WDAzbfoxbroD39+c8LFbRmw6Z9kvZNPu8qBa5WwrYoP5Wt87VGN2Hr6+1Mbc0V7MVyNDXDdmLQ/lO4oDXTY+DqMWzdTUF70amTbIjOxqMH91HDp+p2K48PWinUuO1EMDFwlX3aQgth29VWTYF+bmydrzW6CVtJqqnwcBfM0dQKWzloH7YK2lfFDVqz4f/qK3D1FrZlW9bJ46/mwJyvJ/fvZb9TCVoKWrPhd6wC915lA1cLYZtpauFzdb0W6SpsXZwWUm1VPnvRHEmNsB3KTdFc0JrtNQXuqfPOk/db64Grp7A9dNcd9IuDI2xoztWZdJr8dnzKfq89TQhaU4hx24lo+J3XrAL3R4oFruhh22iqNz1cl7J1vRbpKmwlMZGBtG51K3vxHEXpsOWDtpvdVlR6CVw9he3g3XexgTlf1x87ouiEqYlB+xq7ncjUCFyRw3bDuk75sU6ujtcq3YWtpKQwnb2AjqJk2A7lMUG7XltBayYH7vnaDlw9hW3vffeyYWkPEUMfs989XzZBe5Y2g9ZMDlzTMcjlSQrcdPsGrshhW16SxdbtWqbLsA0O8KCejlr2IjqCUmE7GrQPWn63loPWbO9/39V04OopbBseeIANSnt4aXgn+93zYRu0Z2k6aM1GA/cs+ZhGAzeO3W4uRA3bld0NFBbizdbtWqbLsJVk27FQzpcSYTsxaP+l+aA103Lg6ilsqx98kA1Ke7j16CH2u+dKj0FrZhO499kvcEUN27zsRLZO1zrdhq2n+zJqqi9hL6ba7B22ctA+YhW0r+knaM32/k+bgYuwnRnpmV3uu+diQtC+q5+gNZOOyd6BK2LYtjWVk6+XM1una51uw1aSGBdKmwSYkWvPsB3KS9V90JqNBu758nFqJXARtjPHffdsGSFozYbffd0qcO+ed+CKGLbS45tcXa4Hug5bSWVZDntR1WSvsB3KZ4J2Qw+7rV5oLXARtjNzxYlj7HfPhk3QfkEK2tfZ7fREDlzTscplTArcjLkHrmhhW1uZTy4rFrL1uB7oPmwjQn1pdW8Te3HVYo+wNWLQmsmBe4E2AhdhOzM/ODK/MVsjBq2ZvQJXpLBdu7qVoiMD2DpcL3QftpKC3GT2AqtlvmE7GrSjFaDESEFrtvd//9ZE4OopbGsUDNtn9u1mv3smbIP2C4YKWrPRwP2CfA6O3C8Fbjy73VRECtti0/dzdbeeGCJs/X1cqKOlkr3IaphP2MpB+1nlJxl5/UXDBa2ZFgJXT2Hbef99bFDag/eOzex3TwdBO2b43/MLXFHCtru9hoIC3Nm6W08MEbaStOQo9kKrYa5hO5SfhqAdZ++HYgeunsJ24z13s0E5XxefPEH9H69kv3sqE4LWFDbcdkZiG7j3zCpwRQnbrPQ4ts7WG8OEravzYqqrLmAvttKsw1Z6GbpUyKez27S/R+6+0/I5BO2Y0cC9QD4vx266gfa+/xZ7Dh3h6O23yvulh7A9aDq3/yotpgerq+0qKjeDPXdT2fvhe6Y/rr4r79do0L7B7rsRSefCHLhH77iN9i79L3sOx5POqfQZiaPCtqmuhDzdlrF1tt4YJmwlsVFBNNDfzl50JW2tKrAU6rnY/+yf2d9rZNYVhYhOfONSdr+14Ph132KPSRTStef228jmez8MZSWwv1dJ0mOZ0uOZXF2tR4YKW0lpUQZ74RW1pt3yfNxsHfr5T/jfCbTvub+y50wE0nqk3D5rwaFf/JQ9JhHs/8sf2X2GXvnccOdsWmeeSVu6G9jfqaSK0my2jtYrw4VtSKAn9XbWsRdfSVJh3laaJXcpz1h1Ifu7YMzWuhK554A9fw6yzRF/0NnZtopcy/F8ajrHr63qpqs//njObtm4gYpaam3O06yZ9oPbVxgj3w/cuZvEtvJchwTtqt5GCg/1YetovTJc2EpyMmc/TR7A6Fx3bqGzT59mJz1N5Y4jB6nl0372d4Ix5ecksXWznhkybL09llNzQylbCABgclJo/ubAXjZUx7v0xHHymeMjPqBf7c2V5OfjwtbNembIsJUkxYfTxzp9pzCA0jo+WS23dJ/cv5fuOnKArj5+jL539DA9fGgfvTS8gzK2blB0gXjQLukxTK5O1jvDhq2kqjyXLQwAAGB/dVUF5Oq0iK2P9c7QYRsZ5kf9fc1soQAAAPsZ6G+j2KhAti42AkOHraQwL4UtGAAAYD8lhelsHWwUhg/bAF9X6mytYgsHAADMX09nLQUHerJ1sFEYPmwlGanRbAEBAID5y86IZ+teI0HYmri7LKH6miK2kAAAwNw115eSl8dytu41EoTtZ+Kig2n9mg62sAAAwOxJj1cmxYexda7RIGytlBVnsgUGAABmr6osh61rjQhhayU0yIv6uurZQgMAADO3uq+JIsN82brWiBC24+Q6YKkpAAC9KchNYetYo0LYjuPj6UStjWVs4QEAgOl1tFaRv68rW8caFcKWkZIYQZ9s6GELEQAATC09JZqtW40MYTuJ6oo8thABAMDk6qsLyc1lMVuvGhnCdhJREf60ZmULW5gAAGCi9WvaKS46iK1TjQ5hOwVpkXl0JwMATE+qKwtyk9m6FBC204qJDKDayny2cAEAwGjXMVq0U0PYzoCL00JKTYqktuYKtqABABiRNOtYmgyFMdrpIWxnwdfbmfKyk2hlTwNb8AAAjEB6YYX0HC0e75k5hO0chIf4UEVJFm1c18kWRAAAPZLedSy9ghFvhpo9hO08JMSGUGNtMVsoAQD0RFq9B4sKzB3Cdp483JZSZlosdbXXsAUUAEDLpIXfpfVosUze/CBs7STQ352K8lNpzSo8mwsA2jfQ30YlhekUHOjJ1nkwOwhbO4uO8KcavH0KADSsrqqAYqMC2ToO5gZhqxDp/cqtjeVsQQYAEFF7cyWlJUeRq9Mitl6DuUPYKsjHy4lysxKprxtr5AKAuFb1NlJ+ThL5+biwdRnMH8JWBaHBXlRWnEkb1nawBR0AwBE2DXRRZWk2hYf6sHUX2A/CVkXxMcHUUFPEFnoAADU11ZVQYlwoW1eB/SFsVebusoQyUmOos7WKvQEAAJTU3V5DWelx5Om2jK2jQBkIWwcJ8HWjwrwU6l/ZzN4QAAD2tHZ1KxUXpFFQgDtbJ4GyELYOFhnuR1XluVjKDwAUI61cFh0ZwNZBoA6ErSCSE8KppaGMvVEAAOairalcXrHMZcVCtt4B9SBsBeLtsUJesL63s469cQAAZmJldwPlZSeSr5czW9eA+hC2AgoJ9KTSogwa6G9nbyQAAM6GdZ1UXpJFYSHebN0CjoOwFVhsdBDVVxeyNxUAgDVpBTJpJTKuLgHHQ9gKzs15MaWnRFNHSyV7gwGAsXW1Vcsrj3m4LmXrEBADwlYj/H1cqCA3mVb3NrE3HAAYy5qVLfJKY4F+bmydAWJB2GpMRKgvVZbl0KaBbvYGBAB9+2RDL1VX5FFUhD9bR4CYELYalRQfRs31JezNCAD61NpYJq8oxtUJIDaErYZ5uS+n7Iw46umoZW9MANCHvq56ys1KIB9PJ7YuAPEhbHUgOMCDSgrTad3qNvZGBQBtWr+mQ14xLDTIi733QTsQtjoSExlItVUF7E0LANpSX1NEcdHB7L0O2oOw1RkXp0WUlhxJ7c0V7A0MAGKTVgTLSI2WVwjj7nHQJoStTvl5O1N+ThKt6mlkb2gAEEt/X7O8EliAryt7T4O2IWx1LjzEhypKs2njuk72BgcAx/p4fbe88ldkmB97D4M+IGwNIiE2lBrritmbHQAco7mhlJLiw9l7FvQFYWsgnm7LKCs9lrrba9gbHwDUIa3sJa3w5e2xnL1XQX8QtgYU5O9OxQVptHZVK1sRAIAypJW8pBW9pJW9uHsT9Atha2DREQFUU5nPVgoAYF911QUUGxXE3ougfwhbw1sov/6ttamcrSAAYH6kFbvSkqPI1Xkxc/+BUSBsQebr5UR5WYm0sruBrTAAYHakFbqklbqkFbu4ew6MBWELNsKCvam8JIs2rO1gKxAAmNqmgS55ZS5phS7uHgNjQtgCKz4mhBpqi9jKBAB4TfUllBgXyt5TYGwIW5iUu+sSykiNoa62arZiAYBR0spbWelx5Om+jL2XABC2MK1APzcqykulNStb2IoGwKjWrW6VV9ySVt7i7h0AM4QtzFhUuD9VV+TSJxt62IoHwEhqq/Lllba4ewVgPIQtzFpyQji1NJaxFRCA3rU1V1BqUiS5OC1k7w8ADsIW5sTbcwXlZCZQX1c9WyEB6I20glZ+dhL5ejuz9wTAVBC2MC+hQV5UVpRJ69e0sxUUgNZJK2ZVlGbJK2hx9wDATCBswS7iooOovqaQrawAtEpaKSshNoQt8wCzgbAFu3FzWUzpKdHU0VrFVlwAWtHVXkOZabHk4baULesAs4WwBbvz93WlwtwU6u9rYisyAFGtXdVCxflp8spYXNkGmCuELSgmMsyPqspy6OP13WzFBiCSmoo8eSUsriwDzBfCFhSXFB9GzQ2lbAUH4GjSilfSyldc2QWwF4QtqMLLYzllZ8RTT2cdW+EBqK2vu55ysxLJx8uJLbMA9oSwBVUFB3pSaWE6DfS3sRUggNKkFa3KizPlFa64MgqgBIQtOERsVCDVVRWwlSGAUhpqiig+JpgtkwBKQtiCw7g6L6K05Chqb6lkK0YAe+lsq5ZXsJJWsuLKIoDSELbgcH4+LpSfk0yrehvZihJgrvpXNlNhXioF+LmxZQ9ALQhbEEZEqA9VlmbTpoEutuIEmClpZarq8lyKCvdjyxqA2hC2IJzEuFBqqithK1GA6bQ0lMkrU3FlC8BRELYgJE/3ZZSVHkfdHTVshQowXm9XnbwSlbQiFVemABwJYQtCCwrwoOKCNFq7upWtYAGkFadKizIoJMiLLUMAIkDYgibERAZQbWU+W9mCcdVXF8orTnFlBkAkCFvQDJcVCyk1KZLamirYiheMo6OlSl5hys15MVtWAESDsAXN8fV2przsRFrZ3cBWxKBfq/uaqCA3mfx9XNmyASAqhC1oljQRRlpVqK25AgyguiJPfiabKwsAokPYAgAAKAxhCwAAoDCELQAAgMIQtgAAAApD2AIAACgMYQsAAKAwhC0AAIDCELYAAACK+oj+H1uATMgBRYWEAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\" width=\"238\" height=\"237\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.083px 7.91667px; transform-origin: 231.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to evaluate the complete Figure validation defined in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/spec-v4.1.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpecification\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.25px 7.91667px; transform-origin: 113.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.05px 7.91667px; transform-origin: 381.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u0026lt;= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170.667px 7.91667px; transform-origin: 170.667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValid=check_figureS(hxy, pxy, mseg, epsilon, npxy)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.65px 7.91667px; transform-origin: 97.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCrossing Segments appears in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1720\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody 1720\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242.167px 7.91667px; transform-origin: 242.167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.883px 7.91667px; transform-origin: 375.883px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://poses.live/register\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRegister Team\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 7.91667px; transform-origin: 42.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Anyone can select \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://poses.live/problems\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblems Page\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.35px 7.91667px; transform-origin: 256.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and then click problem numbers to see the puzzles and to download problem files.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function valid=check_figureS(hxy,pxy,mseg,epsilon,npxy)\r\n% hxy hole vertices in order of connection. Last row repeats first for use in inpolygon\r\n% pxy figure original vertices used for initial segment length calculations\r\n% mseg is paired list of connected vertices\r\n% epsilon is allowed stretchiness of segment. hxy,pxy,npxy are all integer\r\n% npxy is figure final vertices used for scoring and Validation\r\n valid=0;\r\n nseg=size(mseg,1);\r\n msegMM=calc_msegMM(pxy,mseg,epsilon,nseg); %Create Min and Max segment integer values\r\n %hplot(hxy,pxy,mseg,size(mseg,1),1);\r\n %hplot3(hxy,npxy,mseg,size(mseg,1),3,segMM);\r\n \r\n%Confirm all final vertices of npxy are in hxy polygon\r\n[in] = inpolygon(npxy(:,1),npxy(:,2),hxy(:,1),hxy(:,2)); % inside or on edge\r\n%check if all vertices are in\r\n\r\n%Confirm all segments are of valid length squared\r\n for i=1:nseg\r\n  nsegL2=0; %calc length squared of segment\r\n  %Check if nsegL2\u003cMin or nsegL2\u003eMax  Min=msegMM(i,1) and Max=msegMM(i,2)\r\n end\r\n \r\n%Confirm all figure segments do not cross hole segments\r\n%Segment/Hole Vertices may touch other vertices and segments\r\n%Intersecting Segments was addressed in Cody 1720\r\n%https://www.mathworks.com/matlabcentral/cody/problems/1720\r\n%A Robust/Fast solution for 1720 was created on 7/18/21 of size 117\r\n \r\n valid=check_intersecting_segments(hxy,mseg,nseg,npxy);\r\nend % check_figure\r\n\r\nfunction valid=check_intersecting_segments(hxy,mseg,nseg,npxy)\r\n%Confirm no figure segments cross hole segments; \r\n % Allowed: \r\n % a) Overlaying segments. \r\n % b) Segments touching hole vertices.\r\n % c) Figure vertices touching hole segments\r\n \r\n valid=0;\r\n nhxy=size(hxy,1)-1;\r\n \r\n for i=1:nseg\r\n  A=[]; % npxy points defined by mseg   A=[a1 a2;a3 a4]\r\n  for j=1:nhxy  %1-2,2-3, end-1 to end  thus why nhxy is 1 less than rows\r\n   B=[]; % hxy points    B=[b1 b2;b3 b4]\r\n   if intersecting(A,B), return;end % intersect detected thus fail\r\n  end\r\n end\r\n \r\n valid=1;\r\nend % check_intersecting_segments\r\n\r\nfunction tf=intersecting(A,B) %\r\n%Correct full solution requires two cross product checks which can be implemented using det\r\n%Segment A [A1;A2],  Segment B [B1;B2]\r\n% Points A1=[a1,a2] A2=[a3,a4] B1=[b1 b2] B2=[b3 b4]  All data in z=0 plane\r\n%p0= B2A1 x B2B1 is det([B2A1;B2B1]) where B2A1 = B2-A1= [b3-a1 b4-a2], B2B1=B2-B1=[b3-b1 b4-b2]\r\n%p1= B2A2 x B2B1 is det([B2A2;B2B1]) where B2A2 = B2-A2= [b3-a3 b4-a4], B2B1=B2-B1=[b3-b1 b4-b2]\r\n%p2= A2B1 x A2A1 is det([A2B1;A2A1]) where A2B1 = A2-B1= [a3-b1 a4-b2], A2A1=A2-A1=[a3-a1 a4-a2]\r\n%p3= A2B2 x A2A1 is det([A2B2;A2A1]) where A2B2 = A2-B2= [a3-b3 a4-b4], A2A1=A2-A1=[a3-a1 a4-a2]\r\n%visualization https://www.desmos.com/calculator/0wr2rfkjbk\r\n%source https://stackoverflow.com/questions/3838329/how-can-i-check-if-two-segments-intersect\r\n% by BenMan95 in ghastly Python not using det or matlab array vectors\r\n%https://www.mathworks.com/matlabcentral/cody/problems/1720\r\n%  Robust Fast solution of size 117 created on 7/18/21 for 1720\r\n%\r\n% Both cross product pair multiplications must be negative for an intersection to occur\r\n% p0p1\u003c0 \u0026\u0026 p2p3\u003c0 for non-endpoint segments intersection. For End point intersection change \u003c to \u003c=\r\n\r\ntf=0;\r\nend % intersecting\r\n\r\n\r\nfunction msegMM=calc_msegMM(pxy,mseg,epsilon,nseg)\r\n%determine Min and Max integer value of allowed length squared for each segment\r\n%abs(Lsqr(npxy,seg(i))/Lsqr(pxy,seg(i))-1)\u003c= epsilon/1000000.\r\n%mseg has indices of connected vertices [nseg,2].  The nseg may exceed number of vertices.\r\n msegMM=zeros(nseg,2);\r\n for i=1:nseg\r\n  Lseg=0; % sum((pxy(mseg(i,1),:)-pxy(mseg(i,2),:)).^2)\r\n  delta=0; % epsilon*Lseg/1000000 and a little tweak\r\n  msegMM(i,:)=[-delta delta]+Lseg;\r\n end\r\nend % calc_msegMM\r\n\r\n%These routines can be used to visualize the data\r\n\r\n% function hplot(vxy,qxy,mseg,Lmseg,id)\r\n% %Need check of segment crossing a hole segment but ignore endpoint\r\n%  [in] = inpolygon(qxy(:,1),qxy(:,2),vxy(:,1),vxy(:,2)); % inside or on edge\r\n%  figure(id)\r\n%   plot(vxy(:,1),vxy(:,2),'k.-') % hole polygon\r\n%   hold on\r\n%   plot(qxy(in,1),qxy(in,2),'b*') % points inside\r\n%   plot(qxy(~in,1),qxy(~in,2),'ro') % points outside\r\n%   for i=1:size(qxy,1)%length(xq)\r\n%    text(qxy(i,1)+.75,qxy(i,2)-1.5,num2str(i),'FontSize',12);\r\n%   end\r\n%   \r\n%   for i=1:Lmseg\r\n%    if in(mseg(i,1))+in(mseg(i,2))\u003c2\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'r-') % segment to OOB pt\r\n%    else\r\n%     plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'b-')\r\n%    end\r\n%    text(sum(qxy(mseg(i,:),1))/2,sum(qxy(mseg(i,:),2))/2,num2str(i),'Color','b');\r\n%   end\r\n%   \r\n%   %o+*.x_|sd^v\u003e\u003cph\r\n%   %colors ymcrgbwk\r\n%    \r\n%   axis tight\r\n%   axis ij\r\n%   hold off  \r\n% end % hplot\r\n\r\n% function hplot3(vxy,qxy,mseg,Lmseg,id,segMM)\r\n%  segMNM=[segMM(:,1) segMM(:,1)+segMM(:,2) segMM(:,2)];\r\n%  [in] = inpolygon(qxy(:,1),qxy(:,2),vxy(:,1),vxy(:,2)); % inside or on edge\r\n%  figure(id)\r\n%   plot(vxy(:,1),vxy(:,2),'k.-') % hole polygon\r\n%   hold on\r\n%   plot(qxy(in,1),qxy(in,2),'b*') % points inside\r\n%   plot(qxy(~in,1),qxy(~in,2),'ro') % points outside\r\n%   for i=1:size(qxy,1) %length(xq)\r\n%    text(qxy(i,1)+.75,qxy(i,2)-1.5,num2str(i));\r\n%   end\r\n%   \r\n%   for i=1:Lmseg\r\n%    d2seg=(qxy(mseg(i,1),1)-qxy(mseg(i,2),1))^2+(qxy(mseg(i,1),2)-qxy(mseg(i,2),2))^2;\r\n%    if d2seg\u003csegMNM(i,1)\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'b-') % segment too short\r\n%    elseif d2seg\u003esegMNM(i,3)\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'r-') % segment too long\r\n%    else\r\n%     plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'g-') \r\n%    end\r\n%    text(sum(qxy(mseg(i,:),1))/2,sum(qxy(mseg(i,:),2))/2,num2str(i),'Color','b');\r\n%   end\r\n%   \r\n%   %o+*.x_|sd^v\u003e\u003cph\r\n%   %colors ymcrgbwk\r\n%   \r\n%   axis tight\r\n%   axis ij\r\n%   hold off\r\n% end % hplot3\r\n%","test_suite":"%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=pxy;\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0+10\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0.001    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0; %non-integer npxy\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16+1    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[15     0\r\n    35    20\r\n    20    44\r\n     0    24\r\n    15     0];\r\npxy=[0    20\r\n    20     0\r\n    20    40\r\n    40    20\r\n    49    45];\r\nmseg=[1     2\r\n     1     3\r\n     2     4\r\n     3     4\r\n     3     5\r\n     4     5];\r\nepsilon=1250;\r\nnpxy=[20    44\r\n     0    24\r\n    35    20\r\n    15     0\r\n     6    25];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n\r\n%%\r\n% Problem 6 shifted up7,left10, 1 seg fail\r\nepsilon=150000;\r\nhxy=[164   164\r\n   121   189\r\n    71   189\r\n    28   164\r\n     3   121\r\n     3    71\r\n    28    28\r\n    71     3\r\n   121     3\r\n   164    28\r\n   189    71\r\n    96    96\r\n   189   121\r\n   164   164];\r\npxy=[36    86\r\n    36   141\r\n    36   156\r\n    41   156\r\n    46   131\r\n    51    56\r\n    56   116\r\n    56   141\r\n    66   116\r\n    71    81\r\n    71    96\r\n    71   131\r\n    71   156\r\n    86    81\r\n    86    96\r\n    86   131\r\n    86   141\r\n    86   156\r\n    91   116\r\n    96    36\r\n   101   116\r\n   106    81\r\n   106    96\r\n   106   131\r\n   106   141\r\n   106   156\r\n   121    81\r\n   121    96\r\n   121   131\r\n   121   156\r\n   126   116\r\n   136   116\r\n   136   141\r\n   141    56\r\n   146   131\r\n   151   156\r\n   156    86\r\n   156   141\r\n   156   156];\r\nmseg=[2     3\r\n     3     4\r\n     4     8\r\n     8     2\r\n     2     1\r\n     1     6\r\n     6    20\r\n    20    34\r\n    34    37\r\n    37    38\r\n    38    33\r\n    33    36\r\n    36    39\r\n    39    38\r\n    33    30\r\n    30    26\r\n    26    25\r\n    25    33\r\n     8    17\r\n    17    18\r\n    18    13\r\n    13     8\r\n    17    25\r\n    10    11\r\n    11    15\r\n    15    14\r\n    14    10\r\n    22    23\r\n    23    28\r\n    28    27\r\n    27    22\r\n     6    10\r\n    10     1\r\n    34    27\r\n    27    37\r\n     5     7\r\n     7     9\r\n     9    12\r\n    12    16\r\n    16    19\r\n    19    21\r\n    21    24\r\n    24    29\r\n    29    31\r\n    31    32\r\n    32    35\r\n    15    19\r\n    23    21];\r\nnpxy=[26    79\r\n    26   134\r\n    26   149\r\n    31   149\r\n    36   124\r\n    41    49\r\n    46   109\r\n    46   134\r\n    56   109\r\n    61    74\r\n    61    89\r\n    61   124\r\n    61   149\r\n    76    74\r\n    76    89\r\n    76   124\r\n    76   134\r\n    76   149\r\n    81   109\r\n    86    29\r\n    91   109\r\n    96    74\r\n    96    89\r\n    96   124\r\n    96   134\r\n    96   149\r\n   111    74\r\n   111    89\r\n   111   124\r\n   111   149\r\n   116   109\r\n   126   109\r\n   126   134\r\n   131    49\r\n   136   124\r\n   141   149\r\n   146    79\r\n   146   134\r\n   146   149];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\n%problem 6 with rotate/shift, 1 seg fail\r\nepsilon=150000;\r\nhxy=[164   164\r\n   121   189\r\n    71   189\r\n    28   164\r\n     3   121\r\n     3    71\r\n    28    28\r\n    71     3\r\n   121     3\r\n   164    28\r\n   189    71\r\n    96    96\r\n   189   121\r\n   164   164];\r\npxy=[36    86\r\n    36   141\r\n    36   156\r\n    41   156\r\n    46   131\r\n    51    56\r\n    56   116\r\n    56   141\r\n    66   116\r\n    71    81\r\n    71    96\r\n    71   131\r\n    71   156\r\n    86    81\r\n    86    96\r\n    86   131\r\n    86   141\r\n    86   156\r\n    91   116\r\n    96    36\r\n   101   116\r\n   106    81\r\n   106    96\r\n   106   131\r\n   106   141\r\n   106   156\r\n   121    81\r\n   121    96\r\n   121   131\r\n   121   156\r\n   126   116\r\n   136   116\r\n   136   141\r\n   141    56\r\n   146   131\r\n   151   156\r\n   156    86\r\n   156   141\r\n   156   156];\r\nmseg=[2     3\r\n     3     4\r\n     4     8\r\n     8     2\r\n     2     1\r\n     1     6\r\n     6    20\r\n    20    34\r\n    34    37\r\n    37    38\r\n    38    33\r\n    33    36\r\n    36    39\r\n    39    38\r\n    33    30\r\n    30    26\r\n    26    25\r\n    25    33\r\n     8    17\r\n    17    18\r\n    18    13\r\n    13     8\r\n    17    25\r\n    10    11\r\n    11    15\r\n    15    14\r\n    14    10\r\n    22    23\r\n    23    28\r\n    28    27\r\n    27    22\r\n     6    10\r\n    10     1\r\n    34    27\r\n    27    37\r\n     5     7\r\n     7     9\r\n     9    12\r\n    12    16\r\n    16    19\r\n    19    21\r\n    21    24\r\n    24    29\r\n    29    31\r\n    31    32\r\n    32    35\r\n    15    19\r\n    23    21];\r\nnpxy=[53   156\r\n   108   156\r\n   123   156\r\n   123   151\r\n    98   146\r\n    23   141\r\n    83   136\r\n   108   136\r\n    83   126\r\n    48   121\r\n    63   121\r\n    98   121\r\n   123   121\r\n    48   106\r\n    63   106\r\n    98   106\r\n   108   106\r\n   123   106\r\n    83   101\r\n     3    96\r\n    83    91\r\n    48    86\r\n    63    86\r\n    98    86\r\n   108    86\r\n   123    86\r\n    48    71\r\n    63    71\r\n    98    71\r\n   123    71\r\n    83    66\r\n    83    56\r\n   108    56\r\n    23    51\r\n    98    46\r\n   123    41\r\n    53    36\r\n   108    36\r\n   123    36];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-18T21:43:20.000Z","updated_at":"2021-07-19T01:11:39.000Z","published_at":"2021-07-19T01:11:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.icfpconference.org/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eICFP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e held its annual 3-day contest in July 2021 with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eHole-In-Wall\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Contest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/spec-v4.1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpecification\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe contest folds the figure in Red to fit within the hole shown in light grey \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"237\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"238\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to evaluate the complete Figure validation defined in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/spec-v4.1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpecification\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u0026lt;= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValid=check_figureS(hxy, pxy, mseg, epsilon, npxy)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCrossing Segments appears in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1720\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody 1720\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://poses.live/register\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRegister Team\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Anyone can select \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://poses.live/problems\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblems Page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and then click problem numbers to see the puzzles and to download problem 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52334,"title":"ICFP2021 Hole-In-Wall: Figure Validation with Segment Crossing and Segment on Wall Checks","description":"The ICFP held its annual 3-day contest in July 2021 with Hole-In-Wall. Contest Specification.\r\nThe contest folds the figure in Red to fit within the hole shown in light grey \r\nThis Challenge is to evaluate the complete Figure validation defined in the Specification when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\r\nValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u003c= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.   4) Pathological cases of Segments crossing Wall region between Hole Vertices or from figure vertices on Hole edges is not allowed.\r\nValid=check_figureSP(hxy, pxy, mseg, epsilon, npxy)  \r\nCrossing Segments appears in Cody 1720 but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\r\nThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use Register Team. Anyone can select Problems Page and then click problem numbers to see the puzzles and to download problem files.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 690px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345px; transform-origin: 407px 345px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 7.91667px; transform-origin: 14px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.icfpconference.org/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eICFP\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.65px 7.91667px; transform-origin: 146.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e held its annual 3-day contest in July 2021 with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eHole-In-Wall\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.95px 7.91667px; transform-origin: 29.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Contest \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/spec-v4.1.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpecification\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 237px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 118.5px; text-align: left; transform-origin: 384px 118.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.267px 7.91667px; transform-origin: 230.267px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe contest folds the figure in Red to fit within the hole shown in light grey \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 238px;height: 237px\" 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C2C2dob50oE//IZOXfxlS5iMjccu1/R4rL1sXtVKu0yV4KFf/YxOn2M9rnsBHfztr2lXkCd9ug7jujB/BbnJbJ2vNboI29AgL+rrqmcvFMBMbOmopd2uS+jwT35M9DluPDaA/Rz00o7YENr/l6fp5KXjxnUfvI/2LP+IBk2tE+5zADOxureJIkJ92bpfS3QRtmVFmexFApjOtvJcGn7/LTp6Gzce+zwNZaHHZKaG8lJo5PUX6dhNtuO6x77/XRp+5zXaVoz7FOamsiyHrfu1RPNhGxcdROvXtLMXCGAy29Niad8/n6Xj37zaJhjGxmML2M/B9LbWl/DjuldeTvv/8RfanhTJfg5gMpsGuikpPozNAK3QdNi6uSymehVe4g76sTPUlw78/gk69eWLLCFgOx6L5RjtZfOqFn5c94Lz6eBvfkW7Aj1p87pO9rMA4zWb/ojzcl/OZoEWaDpspWnh3EUBsCaNx+4x/WF2+JEHLRW+5ORXv4LxWJVMPq57L+1Z/iENNmNcF6aXnRHHZoEWaDZs/X1dqQMP1MMUtpXn0PD7b9LR226xqeAxHus4Y+O619tck2Pf/w4Nv/0qbSvKYD8HIOkx/eEcHODBZoLoNBu2Bbkp7MUA2J4aQ/te+PvE8dgf3k57//suba3CeKyjTTque8XltP/ZZ2hHYgT7OYCSwnQ2E0SnybCNDPOj/r4m9kKAQW3ooZ0hPnTwySfo1EVj47F05pl06NGHabf7ctrSjfFY0diO655tuW6nzj+PDj7xK9plasVsXtvBfhaMad3qNoqJDGSzQWSaDNuqshz2IoDxbGmvoT3Oi+nwww+MBazJyUu+Qgee/h3tjMB4rFZYxnW//n821/LwA/fQnmXSuG4F+zkwntqqAnJxWsTmg6g0F7bS9O+P13ezFwCMY5vpD67h996goz/4vk3FfPzb19K+l56jIbxRTLOGclNo5LV/0bEbx43rfu9mGnn7FYzrgiwtOZLNCFFpKmy9PJZTc0Mpe+LBGLanRtO+F/5GJ665yqYiPvrD22jvf9/BeKyObK0rob0L36cjd99pc61PXP4N2v/3P9OOhHD2c2AM7c0V5OftzGaFiDQVttkZ8exJB51b3007g73p4JOP06mLvjRW8VrGY5dhPFbHNq9sod2mSvXQLx+l02dbjeuedx4dfPyXtMvfnTbjxTaGlJ+TxGaFiDQTtsGBntTTWceecNCnwbZq2uO0iA4/NNl4rD/7OdCvHTHBtP+ZpyaM6x65/x7as/R/NNhUzn4O9GlVTyOFh/iwmSEazYRtaWE6e7JBf7aVZtPwv9+go7fy47HbM9HDYXRDucn8uO53b6KRt16hbagvDKPCVF9wmSEaTYRtbFQgDfS3sSca9GN7SjTte/6vdOLqK20q0LHx2Hz2c2BcW+uKJxnXvQzjugaxcV0nJcSGstkhEuHD1tV5EdVh0ot+re+mXcFedPB3j9GpL104VmHajMdi+USY2uaVzey47unzvkgHH/sF7fJzo839GNfVq0bTH12ebsvYDBGF8GGblhzFnlzQtsHWKtqzYiEdfuj+sYA1OXnJxRiPhXmRxnUPcOO6991Ne5b8lwYby9jPgbZlpceyGSIKocPWz8eF2rHwtK5sK8mi4Xdfp6O3fM+mIjz+rW/Svhefo+2YcQ52Mum47nduopE3X6ahgjT2c6BN3e01FOTvzmaJCIQO2/ycZPakgvZsT46i/c/9lU5cdYVNxXf0jtto+IN3aGslxmNBGWPjuj+0KXsnvnEZ7f/bn2hHfBj7OdCeYtMfUFyWiEDYsI0I9aFVvY3sCQWNGOiiXUFedPC3j9GpCy8Yq+jOOIMO/fRh2u22jLZ0YTwW1GE7rvsFS3k8/cVz6eBjP/9sXBcTMbVs7apWio4IYDPF0YQN28rSbPZkgvhGx2M/osM/vm8sYE1OfuViOvDUb2lnOMZjwbF2RJvHdb9mU0aP3Pcj2rv4AxpswLiuVtVU5psyZOGETHE0IcM2MS6UNplaRdyJBHFtK86k4Xdfo2O3fNemAhsdj/0HxmNBOEM5yTTy6j/p+A3X2ZTZYzffSCNvvERD+ans50BsKYkRbLY4knBh6+m+jJrqStgTCGLanhRJ+//xFzpx5fjx2B/Q8AdvYzwWhLe1tpj2fvQeHfnRuHHdyy6l/X/9I+0wNQC4z4GYWpvKydfLic0YRxEubLPS49iTB2LZvK6TdgV60sHf/JpOXWA7Hnv4pw/RbrelGI8Fzdnc10y7TZX0oV/8lE5/wWpc99xz6dCvf067fF1p8+pW9rMglrysRDZjHEWosA0K8KDujhr2xIEYBlsqac/yj+jwg5ONx/qxnwPQmh3RQXTgz3+gk/83blz3XvO4LlYgE9nK7gYKC/Zms8YRhApbado2d9LA8eTx2HdepWPf/45NxTM2HoseCdCnoZykScZ1b6CRN16koTyM64qqvCSLzRpHECZsYyIDaC26Z4SzIzGC9v/jGTpx5eU2Fc3YeGwe+zkAvdlaW8SO65689Ou0/y9P047YEPZz4Dgb1nZQfEwImzlqEyJsXVYspFpMohHGZlMB3RXgQQef+BWduuD8sYrFZjwWyx2CMW3pa+LHdc85hw796me0y8eFNq9qYT8L6msw/ZHk7rqEzR41CRG2qUmR7EkCdQ02V9CeZR/S4QfuHQtYE8t4bBjGYwGsTTque89dtHfRf2hrPZ6sEEFGagybPWpyeNj6ejtTW1MFe4JAHduKMmjk7Vfp2PfGjcdeew3t+9c/aDtmiANMadJx3ZtuoJHXpXHdFPZzoI6utmoK9HNjM0gtDg/bvOxE9uSA8qQXsUtjTdZLkkmk9xfv/fA9+fV23OcAgCe97lHqHZL+ULW+p6R77MAffktDWajvHKUoL5XNILU4NGzDQrzl6dnciQFl7f3fv20qA8nR22+lnSE+8juNuc8AwMxJryWVupPH32f7Xvgbuz0oa83KFooyXRMui9Tg0LCVpmVzJwWUd/yaqyw3/8lLvkJDmQnsdgAwP1IP0slLx9bWPfm1r7LbgfKqK3Ll7HFxeo+8PJ4gP7/vUmDAFRQcfJEsMPByCvC7nrw8f0Guzm9OyKz5cFjYJsSG0MZ1newJAWXt8ne33Phm0tgsty0AzI/0juXx95u04hW3LShr66c5lJ/3C1OwXkihoQumFBLyBfLzvZ3cXZ9lM2y2HBK2Hq5LqbG2mD0ZoDzpkQXphj9xzdWWN0GdPuss+a043PYAMDd7nBdbHp+T3jxlnkAlrYiFx4PUtX0wnk6e+D/asmUBxcfzAcuRQldqBXNZNhsOCdvMtFj2ZIDyrFu18qom2Ul09PYfyP+WXlyxM9SH/RwAzM6OmGA6/u1r5Xvr2Hdvou3JUTT8n7cs9x9at+rZtcOVTp8+m0wnXtbSwgfrVHy872PzbKZUD9tAP3d5GjZ3QkB55latVAls+2zMfFewF524/DL5/x/94W00lIvHFADmY1tpNh25/x75npLmREiL1kv/f2tdseURO7Ru1bF7hzOdPHmJJWgle/cuoMxMPlSn4u31CJtrM6F62BZhfUiHGd+qtf7Z3oXvE515pvyzg4//kgbxBxHAnEhvmJJeAmO+14bfe9Pm52jdqmfwk0o6dfIim6A1W7mSD9QphZxB7q5/Z7NtOqqGbVSEvzz9mjspoDybVq3pL+/xP9/3wt/ln0ukxQXG/xwApmc9IUpaC3fzWtuJoGjdqmf/yJ/YoJUcPbqASkqYQJ2GNFvZZcV/2IybiqphW12Bl9Y7ylStWjNp+TxpzU5pm9NfwIQpgNna47LEMiHq8E8eoq01Rex2w/9523I/onWrjK2bC4hOn8kGrdnGjQsoMpIP1al4uP+BzbipqBa2KYkR7AkBdUzXqjWznTB1Be0M9WW3AwBb0qo/x6/7lnzvmCdEcdtJ5NbtZ8tVonWrjOE9r7MBO15dHR+oU/HzvYXNuamoErY+nk7U2ljOnhBQ3kxatdZsJkzdeTve6wowjW1l2XTkgYkToqaC1q2yjh65lQ3X8bZvX0DJyXyoTiYk5BxTtn04IeumokrY5mbh7USONNNWrTWbCVNP/JK2tNew2wEY3ea+Zjrw1O/ke0UyfkLUZNC6VdbJk19lw5XT2cmH6lTcXF5i824yiodtaJAX9XXVsycDlDfbVq012wlTz7HbABjdyJsvW+4TbkLUVNC6VcbgJ9WmED1jQqhOZv/+BZSXx4fqZDzc/spm3mQUD9uy4kz2ZIA6LK3a674141atme2EqS/QniX/ZbcDMKrdrkvo1IUXyPfIVBOiJrO1rgStWwUMflrGhupU1qzhQ3Uy7iKFbVxMMK1f08GeDFDefFq1ZqMTpm6Vf4e09B4WkAcYtSM2lI5fP7MJUVMZ/gCtW3vb/HEznT59Lhuqkzl1agFVVPDBynF3/Qebe5NRLGzdXZZQwyz/ygP7mk+r1pr1hKkjd91BQ3gxCRjctrIcOvzAvfI9MdMJUZNB61YZ0nuQpRCdjc2bF1BsLB+u47k6vcVm32QUC9uM1Bj2BIA67NGqtWY7YepXmDAFhrV5ZTMdeHr2E6Kmgtat/R3Y/wQbqNNpbubD1VpgwJVs7k1FkbAN8HWlztYq9gSAOuzVqrVmM2HqJUyYAmMaeWvuE6Img9at/e3ZuZgN0+ns3r2AMjL4kDXz9b6Hzb6pKBK2hXgu06FsWrVvvsxuMxc2E6bO/gLtWfo/djsAvdrtupROXXihfA/MZULUVNC6ta+tm/Pp2FHTHzBMoE6nt5cPWUlw8Hnk4fYMm31TsXvYRob5UX9fM3vwoA4lWrVmNhOmrr6SdoZjwhQYw444aULUt+WyP58JUZPZWi+1br8r/360bu1j7+5/s2E6nSNHFlBRER+2vj53stk3HbuHbVV5LnvQoA6lWrXWMGEKjGabqV47/KB9JkRNBa1bO9vUZQrO29lAnc6GDQsoPNw2aIODLyIXp3fZ7JuOXcM2OSGcPl7fwx80qELJVq01mwlTv/k1bemoZbcD0DqphXngj0/KZV1ijwlRk0Hr1v6GBpPp6JHb2ECdTm2tVdAGfZk83J9is28m7Ba23h4rqKWhlD1YUIcarVprNhOmXn6e3QZA60beesVSzu01IWoqaN3a3/atkXT40INsoE5l27YFlJQkzT6+nDzdn2Szb6bsFrY5mfHsQYJ6bFq1Zcq1as1sJ0ydjQlToDu73ZbSqS9ZT4gqZLezJ7RulSG96GL/vqenXXZvvIb622f9TC3HLmEbEuhJvZ117AGCOtRu1ZrZTpi6inaG+7PbAWjNjvgwOn7DdXLZVmJC1FSGP3jHcj+jdWtf27Zk0qEDP6PTp77IhqvMFMhHDt9FO7aF0qreRooI9WGzbzbsEralRRnsQYF6bFu1Oew2SrGZMPWjH9JQQRq7HYBWyBOiTK1KqUwrOSFqMnLr9ha0bpW0eVObHKZ7di6ikb0vyvbs+pB2bveRW8HW21aWZrPZNxvzDtvYqCAa6G+32TFQl6NatdZsJkz9FhOmQLs2r2pVbULUVNC6FcemgS5KjAtlM3Cm5hW2rs6Lqa5a+TEMmJqlVXu9+q1aa7YTpl5gtwEQ3cjbr1rKsRoToiaD1q1YmupKyNN9GZuFMzGvsE1PUW8MA3gitGrNbCZMnXMO7Vn2IbsdgKh2myrTUxd9aTTgVJoQNRW0bsWSlR7HZuFMzDls/X1cqMNUuXI7BOoZa9V+26GtWjObCVPXXEU7IzBhCrTBkROiJrO1vhStW4F0d9RQUIAHm4nTmXPYFuQmszsD6hGpVWvNZsLU3dKEqXR2OwBRbK3IM4XZ/XKZdcSEqKns/S9atyIpLkhjM3E6cwrbiFBfWt3bxO4IqEe0Vq012wlTj9EWPBoGgtq8upUO/On3lkBz1ISoyQyaWrdH0boVxlpTeYmJDGCzcSpzCttKwSp2I7Jp1b4lTqvWmvWEqZFXMGEKxDQsyISoqaB1K5baynxyWbGQzcfJzDpsE+PC5GnQ3A6AekRu1ZrZTJg69xzas/wjdjsAR9ntvpxOffkiuYyKMCFqMqOt2++N7idat0JITYpkM3IyswpbL/dl1FRfwn4xqEcLrVoz6wlTx795Ne2MCGC3A1DbjoRwOnbj9XLZFGVC1FTQuhVLW1MF+Xo7s1nJmVXYZmfEsV8K6tJCq9bariDrCVN30rZCTJgCx9pamUeHHxJzQtRkBhvQuhVNnqkxwWUlZ8ZhGxzgQT14K5DD2bZqX2G3EZHNhKnfPUZbuurZ7QCUtnl1Gx348x8s95FoE6KmgtatWFb2NFBYiDebmePNOGzL8P5jIWitVWvNZsLUq/9ktwFQ2vA7r1nKoagToiaD1q14pGzkMnO8GYdtW3MF+0WgHq22as1sJ0ydiwlToLrdHtYTon4s7ISoqaB161ir+5rk1xRnZ8TLj8G6Oi9iM3M8hK2G2LRqy7X5+NWECVORmDAF6tiRGEHHbtLOhKjJoHWrrvVr2qnFdM4Lc1MoNjqIvEx/sHEZOR2ErUZovVVrzWbC1D130TYMUYDCtlbm0+GHHpDLnFYmRE1l73/ftdQHaN3a1ycbeqiztYrKijMpOSGcAnxd2UycLYStRti2anPZbbTEZsLUk49jwhQoZnO/didETUZu3d6K1q299Jnqn+qKPMpIjaFQU2OAy8D5QthqgJ5atdYwYQrUMPyudidErfx4FVVtXkup2zbIajevof6PV8o/Q+t27taY/jhpqC2i3KxEiorwJ3fXJWzu2RPCVgP01qo1s5kw9cUv0p4VC9ntAOZqt+cKOnXxl+UyppUJUVLA/m/3NrrjyEH6/OnTZIpTG2eb/t+9hw9QQE8bHUHrdkY2ruuktqZyKs5Po4TYEPL1cmJzTkkIW8HptVVrZjNh6tpraGdUILsdwGyNToi6QS5bWpkQ5bRrkC4+eWJCwE5mibub6T9M/2WC1q2t7vYaqijNll+rGGSqR7lcUxPCVnCWVu0N1+mqVWvNZsLUvZgwBfO3taqADj+snQlRUvfwn/ftZgN1Klds3kzNd91l+ofpj/GH7jd063ZVTyPVVuXLC7yHh/iQi9PsFgpQGsJWYHpv1VqznTD1BG3pbmC3A5jO5jXtdOCZpyz3jugToqQx2FuPHmLDdCbe9vQ0/Yfpv0x2uhundbuuv01+V39+TjLFRAWSp+nYuewSBcJWYEZo1VqzmTD12r/YbQCmM/zu65ZyJPqEqDWmoH1mDi1aa1LrtulHPzL9YwGt/Okjum3dfry+mzpaKqm0MIOS4sPI38eFzSpRIWwFZdOqfVvfrVozmwlT532R9jhhwhTMjjQh6qSGJkRJY7Tjw3Mu3vLyMv2H6b9MGn3c2e/Sot7OOqoqz6H0lGgKCfRks0krELaCMlqr1mwoO3FswtS3vkk7o4LY7QDG254UScduvlEuO1qYEFW+ZR195+hhNjxn6/ItWyyt2+afPUrdazrY7xRdf18z1Zv+QMrJTKDIMD9yc1nM5pEWIWwFZMRWrTXbCVM/om3Fmex2AGbyhKhHHpTLjFbeECU93jM+NOfDunVb5evBfqdoNqztoJbGMirMS6W46GDy9lzB5o8eIGwFZNRWrTXrCVMHfv8EbenBhCngbTa14vZraEKU2UOH9rGhOVfWrduuR38i7NhtV1s1lZv+gE5JjKBAPzc2b/QIYSsY21btq+w2RmEzYer1F9ltAIb//YalnGjlDVHSiyu4F1bMl3XrVpTnbld2N1BNZR5lpsVSWPDM1n7VI4StYNCqHWM9YerUeefRHqdF7HZgXLu9nOjkVy6Wy4iWlswrHBxgw3K+rFu3+37smOdu165qpca6YsrLTqLoiADycFvKZorRIGwFglbtROMnTO2IxoQpGCVPiPqOdiZEWUvctpENS3tQu3W7aaCL2k35UFwgvQoxlHy9ndkMMTqErUBsWrUVxm7VWrOZMHXf3bStJIvdDoxja3UhHX7kx3KZ0OKSeXHbNrFBaQ/WrVul3pnc01FLlaXZlGb6Ayc4wIPNDLCFsBUEWrVTs50w9Rva0tPIbgf6t3ltB+3/y9OW+0WLS+aVbFnHBqW9vGvn1u3q3iaqqy6g7Ix4igj1JVenRWxOwOQQtoKwbdXmsdsYHSZMgWT4Pe1NiBpPekWjtHqPORzt7QeffExHf/B90z/m1rod6G+n5oZSKshNptioIPLyWM7mAswcwlYAaNXOjM2EqfPPoz3OmDBlNLu9nOVuYzlENDQhivPzgyNsUNrD3/btpr3/+7fpH6Z/mUzXuv1kQw91tlZRaZH0KsRw8vd1ZXMA5g5hKwBzq/bYjdfRVrRqp2QzYerb19KO6GB2O9AfaQLUse/cNHqvaGxCFMder2rkxA1tosHGsilbt31d9VRdnksZqTEUGuTF1vtgPwhbB7Nu1Q6jVTsjmDBlPFILVmrJStdcixOiOI2frqEfHjnIhuV8/MzUYpYWOJC+w7p1u235R9RQW0S5WQkUFe5P7i5L2LoelIGwdTC0amdGWnJvKCeZdvm6yl3t5r/YhXTmmbTvpefY49CC4fffpNOf/zx/bAI49r2b5TIglQWpTGh5Ocbg7Z+wgTlX0osycgbXy797w9pO6s5NpuEbrjP9cAF9fOP15LHoP2z9DspD2DoQWrW2xgfqwcd/SUdv+R6d+vJFlvOkFSe/egl7jFpw8rJL2WMSmVRGpLIilRmtBfELIzvZ4JyLl9avpoqSLEpNiqRAU/0i1d0Vn/1BLyn43WMT6nZQB8LWgcZatdcbplVrl0A1tRyPX3uNzPz/Rt54UQjHr71a3h+p5c0dvxYceeAe+RikrnruGB3BfJ1PXHXF6HX/7DGwmRA9iDdu6qO7jhxgw3NaIyO0YP16WtDYSLelJJLLioUT6u6A99+kwSsvN228gDZc/220bh0EYesgem7VDjaU0vaUaNrtsYJG3npFfi72yN0/pBPSDX/GGZbjnsqpCy+gYzddL4/T7X/2Gdr74Xu0M8SHhgrSLJWk9P/M24/fB0cxjyseufN29udaIOIxmK+zFLzSv7f0NtG2wnTaGeYrP4O9/7m/0KFHH5aX2Dt10Zcs20/nxOXfoCN33UEHf/e46Xe/RLvdl8lvptpaVzxhH5TU8clqenF4J5013eNAhw/Tgk8/pQXt7bSgsJAWxMTQF0OC6RFvd1o0xbOvaN06HsLWQbTeqrUEqqeygToVhK0ytBC2U5kQxP+YQxB/7nNjQfzk+CAuYb/XHnx2bKb7D+8fC9eTJ2nB0BAt6O2lBeXltCApiRaEhlrc7OdDf3F3Yutsa2jdOh7C1gFsWrXviNuq5QP1ztkHqukPitFA/fOsA3UqCFtlaD1sp2KXFvFkQZwcZZcg7uyqp0UNlXRfSQGdn5ZqE66SLwUH0R2+XvSs++zWfq34JVq3joSwdQCRWrWTB+oVRGc6PlCngrBVhp7DdirKtYiXTxnE/X3NVF9dSDmZ8RQZ5kduzott6t5lKxbSe85LZCuYMdmZQuvWsRC2KrNt1b7GbmNvgw1ltD3VKlD/YB2oM5to4qhAnQrCVhlGDdup2C2Ir/gGHTad152/fJQG/vR7anj+b5T28vMU+O/X2XrX3tC6dRyErcqUatWOBmrMxEC9apaBahlDFSNQp4KwVQbCdnbsEcSnTUE8/OWL6JNvXk29t91CdQ8/QPmmlnHC83+1axCPtm5NdYLpO9G6VRfCVkXzbdWOBaoTjbw9j0C1tFBnPylJJAhbZSBs52+l6V6qMf0xnRsbTBkf/psynnmKyn/1KLXecxetu/kG2n7Z1+nIuedajmsqkwbxC3+bUxCjdesYCFsV2bRqK/lWrfQ+07FAfdUOgSp+C3WuELbKQNjO3tpVrdRYW0x52YkUHRFAHq5L2XrUmtfC9yjytX9ZgrhtrkF88eyCGK1bx0DYqsS6Vbvvn8+OC9Tf0pF7EKizhbBVBsJ2ehvXdcl1YrHpfkuIDSFfL2e23pwr+wXxl9kgbnjofst2aN2qA2GrkhPf+OwVeDMMU5lpW+ltOYdNN4YcqIs/oB3RQbS1qoD9DqNB2CoDYcvr7qilitJs+VWIQQEebD2plpC3X6HUv/+Jyn79M2q7+05ab2qh7v7qJXRqho/kSczbHrzgfLRuVYCwVcFgfcmEgm6BQJ0zhK0yELajVvc2UZ3pPszOiKOIUF9yneINTSKZSxAnm+oe7neB/SBsVbC1tthSqKVQRaDaB8JWGUYN24H+dmquL6WC3GSKjQokL/flbF2oZdZBvPbmGyznNfLVf7Lbg/0gbFVgHbbSuCq3DcwewlYZRgnbj9d3U0drFZUWZVBSfBj5+7iydZ9eJT7/V8t5RdgqD2GrAoStMhC2ytBz2PZ11VNVeS6lp0RTSJAXW9cZBcJWXQhbFSBslYGwVYaewnbNyhZqqCmi3KwEigr3I3eXJWz9ZkQIW3UhbFWAsFUGwlYZWg7bDWs7qLWxnIryUyk+Jph8PKdfEceoELbqQtiqAGGrDIStMrQWtl3tNVRekkUpiREU6OfO1l8wEcJWXQhbFSBslYGwVYboYbuqp5FqK/MpMy2WwkK8TfXT3FfCMTKErboQtipA2CoDYasM0Y5h3epWy3XufvwX5Om2jK2jYHYQtupC2KoAYasMhK0yHH0Mmwa6qL25kkoK0ykxLpT8vF0s17n+oQfY+glmD2GrLoStChC2ykDYKsMRx9DTWUeVZTmUlhxFwcyrEM3XGWFrPwhbdSFsVYCwVQbCVhlqHEN/XxPVVxdSTkY8RYT5kqvzYrbeMTNfZ4St/SBs1YWwVQHCVhkIW2UocQzr17RTS0MZFealUFx0EHl7rGDrmcmYrzPC1n4QtupC2KoAYasMhK0y7HEMn2zooc7WaiorzqTkhHAK8J3fqxDN1xlhaz8IW3UhbFWAsFUGwlYZcz2Gvu56qq7Io4zUGAq186sQzdcZYWs/CFt1IWxVgLBVBsJWGTM9hrWrWqjRVLbzshIpKsKf3F2VexWi+TojbO0HYasuhK0KELbKQNgqY7Jj2Liuk9qaKqi4II0SYkPI10u9VyGarzPC1n4QtupC2KoAYasMhK0yrI+hu72GKkqzKTUpkoL8HfcqRPN1RtjaD8JWXQhbFSBslYGwtb9VvY20+5675GPYdt23yMVpEVsfqM18nRG29oOwVRfCVgUIW2UgbOdvoL+NmutLqSAnmWKjAsnTfRmtu+n60XN6zVVsXeAI5uuMsLUfhK26ELYqQNgqA2E7ex+v76aOlkoqLcqgpPgw8vdxmXCvI2yNAWGrLoStChC2ykDYzkxvZx1VledSeko0hQR6sve3NYStMSBs1YWwVQHCVhkIW17/ymaqryminMwEigz3IzeXqV+FOB7C1hgQtupC2KoAYasM67DdnhQphKO33yrvj5phu2FtB7U2llFRXirFxwSTj+fsXoU4njlst1/6f3KFLALzdUbY2o/1eUXYKg9hqwKErTL2PTdWWYjm1AXns/tsL11t1VRekkUpiREU6OfG3rNzdfD889ljEkHfD77P7jPMHsJWXQhbFSBslbHHeZHlvArnzDPZfbYXJcP2xFln8cckgKqfPcLuM8wewlZdCFsVIGyVsz01hnbEhLBduo4w8vLzlmst/ZvbZ3uz7kaOiwkm73l0I0db7X/bPXdaunEdLeXZP1Psv55l9xnmRjqv5muNsFUewlYFCFvj2FaaTafPOUe+1sP/fYfdRmn9fdIEqcLRCVJhs5sgVfzELy1lNealf7DbgD4gbNWFsFUBwtZYjt7xA/laH/r1z9mfq2300Z+cGT360/3ZvkuTo1yW/Y/dBvQBYasuhK0KELbGsv/ZZ+RrfeKaq2hLXxO7jaNYXmpRmC6/1MJv3Esthi67VN73nttvsfn/oD8IW3UhbFWAsDWW3Z4rLNd7h0rjtnO1bnUbNdWXUH5OEuV/9L5lv0se+zlbD4B+IGzVhbBVAcLWWGzGbT9wzLjtXOxZPvbyiGrnRRRuKqsuKxay9QFoH8JWXQhbFSBsjUe0cduZOPD07+R9Pnbj9fTpQJf8/+Ql9kqy5CX2Ah24xB7YH8JWXQhbFSBsjUfkcdvJHPvOjfI+H/jDb9ifb1jbSa1N5VSUL72pKoR8VFw8HuwPYasuhK0KELbGYzNumxjBbiOSoZxky/7uWfo/dpvx1qxsoYaaIsrNSqCocH9yd1nC1h0gJoStuhC2KkDYGo/tuO3b7DYisR6vHcpKZLeZTl9XPVWbVxcK8mLrERAHwlZdCFsVIGyNSUvjttx47XzIjxi1Vlmtm+vK1ivgOAhbdSFsVYCwNSbLuO3VV9GWXoHHbTf0TDteO18D/W3UXF9KBbnJFBsVSF7uy9l6BtSDsFUXwlYFCFtj0sq47VzGa+drdW8j1VUVUHZ6HIWH+pCL0yK23gHlIGzVhbBVAcLWmLQybmuP8dr56u6opQrT+ZIeMQrCI0aqQNiqC2GrAoStcY2N2/6M/bkI7D1eO18b13VSW1MFFRekUUJsCPniESNFIGzVhbBVAcLWuIQft5XGa29Wdrx2vtauaqFG0z2UZ2p1R0X4k7srHjGyB4StuhC2KkDYGpfo47ZDOUmW/VNrvHa++rrrqboijzJSYygUjxjNGcJWXQhbFSBsjUv0cds9yz+0lE1HjdfOxyemlnlnaxWVFWdSckI4BfjiEaOZQtiqC2GrAoStsVnGbX8l3rjtgafEGq+dr/Vr2qmloZQKc1MoNjqIvDzwiNFkELbqQtiqAGFrbGPjtlfSlt5GdhuH0MB47Xyt7muiuuoCys6Ip4hQX3J1xiNGZghbdSFsVYCwNTZRx221OF47Xz0dtVRZlk1pyVEUHODB1nVGgbBVF8JWBQhbY7MZt/2POOO2e5Zpe7x2vjYNdFG7qV4rKUijxLhQ8vV2Zus+vULYqgthqwKELYg4bnvgqd/K+6SX8dr5WruqlRrriikvO4miIwLIw20pWxfqBcJWXQhbFSBsQbhxWwOM187Xyu4GqqnMo8y0WAoL9mbrRS1D2KoLYasChC3YjNsmhLPbqGnI1Hoz749Rxmvnq6utmsqLMyklMYIC/NzYelJLELbqQtiqAGELoo3bGn28dr7Wr+mglsYyKsxLobjoYPI2/THF1ZsiQ9iqC2GrAoQtSEQat8V4rX319zVTfXUh5WTGU2SYH7k5L2brUZEgbNWFsFUBwhYkNuO2PQ4ct13fTcduvkHeF4zXKqO3s46qynIoPSWKggM92TrV0RC26kLYqgBhCxJRxm0xXquuTQPd1N5SSSWF6fIjRn4+LmwdqzaErboQtipA2ILEdtz2LXYbNWC81rHWrW6jproSys9JopjIAPJ0W8bWuUpD2KoLYasChC2YiTBui/FasazqaaTaynzKSoulcFP94Lxi4YT6VwkIW3UhbFWAsAUzy7jtVQ4at5XGa2/CeK3IutprqLwkS37EKNDPna2P7QFhqy6ErQoQtmDm6HHboexEy/djvFZ8G9Z2UGtjORXlp1J8TDD5eDqx9fNcIGzVhbBVAcIWzBw9bovxWm1bs7KZGmqKKDczgaLC/cjNZQlbX88EwlZdCFsVIGzBmmXc9pePsj9X0oE/YLxWT3q76qiqPJfSU6IpZJaPGCFs1YWwVQHCFqyNjdteoe64LcZrde1j0/XtaKmk0qIMSooPI/9pHjFC2KoLYasChC1Yc9S4LcZrjWWgv42a60upICeZYqMCydPd9hEjhK26ELYqQNiCNZtx2/fVG7eVAtZcDjFeazyrehuptqqAstLj5EeMkp7/m6U8IGyVh7BVAcIWxnPEuK1lvPYmjNdCL6031UXmeinN9EcfV++D/SBsVYCwhfFsx20b2G3sCuO1MM72pEhLvbQlJ5namsqpOD+NEmJDyMfLfo8YwSiErQoQtjCezbhtfBi7jT1J3cbm78N4LUisw3aoIM3mZ2tWtVBDbRHlmspNVLg/ubvO/REjGIWwVQHCFsZTe9wW47Uw3lRhO15fVz1VV+RSRmoMhQZ5sRkBU0PYqgBhCxw1x22lrmPpuzBeC2azCVtrn2zooc7WKioryqDkhHDy93VlMwNsIWxVgLAFjs24bbeC47YD0njt9fJ3YbwWzOYatuMN9LdTc0MpFeRKjxgFkZfHcjZDjA5hqwKELXDUGrfFeC1w7BW2463ubaK66gLKzoijiFBfcnVaxGaK0SBsVYCwBY7tuO2b7Db2gPFa4CgVtuP1dNRSpamspyVHUXCAB5svRoCwVYFewnaL6abZERUo36RKkVt4BhpTNI/bHv3hbez5sIfD998jf4eh3odsOs4dMSHs+bCXHVFBtKW1iv9+DZCOwVwvKRm21jau65KzpNj0fQmxoeTr7czmjR4hbFWgh7DdWlVAdMbnLMehpOPf+ia7D3p09PZb2XOghGPfuZHdBz06+oPvs+fA7j73ORrKS2H3QXSOCNvx1q5qpUZT/ZiXnUjREQHk4bqUzR89QNiqQA9he8TU8jIfg+LOPJM2r2xm90Nvjptam+w5UIA0EYvbB73Z3N9GdNZZ7DlQwrHvfUeTPQYihO14K7sbqKYijzLTYigs2JvNIq1C2KpA62G798P3LPt/8De/tnSj2dvw269avmfP8o/YfdGTrXXFdOLyy0bP689/wp4Tezj428fk7zj15YtoW3Emuy96stvLyVKO9r3yPHtO7OHAU6Ovv5QMv/s6uy8ik47BvP+ihK01+RGjtmoqM5VZ6RGjAD83Npu0AmGrAi2H7fbUaLlbV9r3ww/cS4MNpex29iA9/iKNK0rfdejXP2e30ZPdbsvGykW4P7uNPVhXqnsXf8BuoyfmEJRa8oONZew29iDNYTj0s0dGv8v0R5M0RsxtJyrRw3a89WvaqaWhjArzUiguOoi8PVawWSUqhK0KtBq2m1e30sEnfiXv98mvXEw7g73Z7exp/7N/Hv2+r11CWyvy2G304uDvRlucx757k+Ld5kfvvF3+rkOmFjT3c70YbCqnE1dfKR+rtPACt4097YgJphPfGO2dkIJXCmBuOxFpLWzH6+9rovrqQsrJiKfIMF9ydV7MZpcoELYq0GrYWncfj7zyAruNvUnnx/yde1YsZLfRA+su5H3P/43dxp5G3nhR/i69dyXv9na2lB+pO5nbxt6G33nN8p1a6k7WetiO19NZR5VlOaOPGAWK94gRwlYFWgxb6+7jI/ffQ4P1ynUfW7PuSj74mH67ktXqQjYzSlfygad/Jx+j0l3I1uTu5EcfHv1eDXUn6y1srW0a6KL25koqKUynxLhQ8hPgESOErQq0FrbW3cenLv4y7VKh+9jaWFfyV2lrZT67jdap2YVspveu5EFTHXXimqvkY1SjC9najuggOnHZpaPnVyPdyXoO2/HWmeq0proSys9OopjIAPI0/bHL5ZySELYq0FrYWncf73tZne5jazZdyU7660pWuwvZTO9dybt8XCzlRq0uZGvD74zNptdCd7KRwna8lT0NVGP6Qz4zLfazR4wWTsg8e0PYqkBLYWvbfXw3ba0vYbdTkm1X8i/YbbRM7S5kM713JR/445PysanZhWxtS3sNHfrpQ6P7oIHuZCOH7XhdbdVUXpJFKYkRFKjQI0YIWxVoJWxtuo9NrZ9dQV7sdmqwdCX/39doa5W+upId0YVspteu5MHmSjr+zavlY1O7C9ma9ArHk5d9ffQcC96djLDlbVjbQa2mP9aK8lIpPiaYfDzt84gRwlYFWglb2+7j59lt1GLTley8iN1GixzVhWym167kXT6ulvLiiC5kayNWL2cRuTsZYTsz/aY/iOtrCiknM4Eiw/zIzWVujxghbFWghbC16T6+7245FLjt1GLTlfz4L9lttMhRXchmeu1KPvDH38vH5KguZGuDbdV0+CfW3cnB7HaOhrCdm97OOqoqz6H0lGgKCfRk85Iz47CtKM1mvximJ3rYTug+NhUgbju1WbqSv/5/8kII3DZa48guZLMjOutKHmyppOPXXiMfkyO7kK3tjAqkk5eK3Z2MsLUPaQUjLjPHm3HYhgZ5UV9XPftlMDXRw9am+/il59htHMG2K3kxu42WOLoL2UxvXcm7fMXpQrY28tYrlv0SsTsZYTt/q/uaKCLMl83M8WYctpLcrAT2C2FqIoetTffxvT+S95XbzhFsupJNLW9uGy1xdBeymd66kg/8SZwuZGuj3ck/Ht03AWcnI2znryA3mc1KzqzCVpqVJc3S4r4UJidq2Np0H1/0JWG6j61ZupIv/TptrS5kt9EKEbqQzfTSlTzYWiVcF7K1nZGB8jCIfK4F605G2M5PR0sV+fu4slnJmVXYSqSljqSlj7gvB56oYWvTffyiON3H1my6kl2WsNtogVQGROhCNtNLV/IuPzdL+RCpC9nayFsvW/ZRpO5khO38SBOkuIyczKzDVlKt89VY7E3EsJ3YfVzEbudoNl3Jv/k1u40WiNKFbKaXruQDf/6DfAyidSFbk1rfhx95cHQ/BepORtjOnbTakNssVxmaU9hGmSqLNStb2J2AiUQLW5vu4y9dSLsCPNjtRGHuSj5x2ddpa42YfxRMR6QuZDOtdyVLY6LmPxhF7EK2tjMigE5+/Wuj51uQ7mSE7dxI6+pK6+ly2TiVOYWtpCg/ld0RmEi0sN37kXX38T/YbURi3ZW823Upu43IROtCNht54yV5n7TalbzL332sXAjahWxt5E2xupMRtnNTWpTBZuJ05hy20vsjpfdJcjsDtkQKW5vu43vuMrUUxZ90ZNOV/NvH2G1EZtOFHOH4LmQzrXcl73/mKXnfRe5CtiY9D3z4YXG6kxG2s9fbVUchQTN/kYW1OYetJDMtht0hsCVK2E7oPja1DLjtRLT/2Wfk/T7xjUtN51NbXckidiGbabUrWXrp//FvXyvvu+hdyNakP7ak933L51zqTu50XHcywnb2pFc2clk4E/MKW3fXpdRgChJup2CMKGFrM/v4X8+y24jKpivZTTtdyaJ2IZtptStZmmdgKQ8a6EK2Zj7nEkd2JyNsZ6eloYy8Pea+KMG8wlYSHxNCG9Z2sjsHo0QI2+2pMWPdx3ffqblnVm26kk0tRW4bEYnahWym1a7k/X95Wt5nrXQhW5NWKDr88AOj++/A7mSE7cxJj7tKj71yGThT8w5bibQOILeDMMrRYWvTfXzhBZrqPrZm6Uo2VVCOXihhpkTuQjbTWleyNJP3+HXfkvdZS13I1qTHv05+7auj591B3ckI25mrLs9ls2827BK20kr3K00tD24nwfFha9N9/E9tdR9bs+lKdl/GbiMS0buQzbTWlSy96cxSDjTWhWzN/GIRiSO6kxG2M7PG9EdyVLgfm32zYZewleRlJ7I7Co4N24ndx9pdPcemK/nJx9ltRCJ6F7KZ1rqS9//1j/K+arEL2dpgcwUdfuj+0WNxQHcywnZmCvNS2cybLbuFra/pL8y2pnJ2Z43OUWFr0318wQXyq+247bTE0pV8xTdoa10Ju40otNCFbKaVruQtnXV0/Ppvy/uq1S5kazvD/Ojk1y4ZPfcqdycjbKfX2VZNAaZ6k8u82bJb2EpSTReP22Gjc1TY2nYf/53dRmtsu5KXs9uIQCtdyGZa6UreFeQ1dv013IVsbeR1x3QnI2ynl5Eaw2bdXNg1bJ1XLKSaynx2p43MEWFr0338ox/qZvF1267kJ9htRKCVLmQzrXQl7//bn+R91HoXsrXBpnI6/GP1u5MRtlNrqCkid9clTM7NjZ3D9iOKjgigtata2Z03KrXD1rb7+Hx5cW1uO60a60q+nAbrS9ltHG2sC/lm4buQzSxdyT97hP25o23pqqPjN1wn76MeupCt7QzzpZNfVbc7GWE7uQ1rOyg+JpjNuLmye9hKinHhbKgdtjbdxy+I34U5WzZdyR4r2G0cSWtdyGaidyXvCtZfF7K1kdf+ZTk+NbqTEbaTKzeVfy7b5kORsA3yd6fu9hr2IIxIzbC1effxXXfQVh1268tdyTeNdiUf+P1v2G0cSWtdyGaidyXv/7v+upCtDTZK3cn3jR6jCt3JCFten6l+CQ32ZrNtPhQJW0lWeix7IEakVtjadB+ff57uuo+tWbqSrzRVvA1idSVrsQvZTNSu5C1d9XTsRn12IVvbGepLJy/5iuUaKNmdjLDl5WYlspk2X4qFrafpr/smwR/NUItaYWvTfayh7su5sOlK9hSnK1mrXchmonYl7zS1NCzXW4ddyNZGXlWnOxlhO1FrUzn5mMoXl2nzpVjYShLjQmnjQBd7UEaiRthO6D6uyGO304vRWcmjLZ1jN98gv41HBId/8uOxa62hLmQz6wr4yIP3ssfoCEdv+a68T3rtQrYmHd/hB5XvTkbYTpSSGMFmmT0oGraSitJs9qCMRI2wlVpR5u+QbiJuG705cu/dlmMWzelzz2X3WQuk92dzxySCo7fdwu6z3kj1xMmvXCwfs/S4E7fNfCFsbdWYGihchtmL4mEbbio0q3oa2YMzCjXCdkd0kPxX//AHb7M/1yOpsjh91lmWcyuMz32ODvz5D+w+a8HIKy8QnXEGf2wOdPqsz9POyAB2n/Voz7IP5Xtasd4whK3F2lUtFB3hz2aYvSgetpL8nCT2AI1CrTFbAICZQtiOKc5PY7PLnlQJWz9vF2pvrmAP0ggQtgAgGoTtqK72Ggr0d2ezy55UCVtJWnIUe6BGgLAFANEgbEdlpsWymWVvqoWtq9MiqtPJ+3lnC2ELAKJB2PZSY10xebgtZTPL3lQLW0lMVCCt629jD1rPELYAIBqjh+3GdZ2UEBvCZpUSVA1bSUlhOnvgeoawBQDRGD1sK0qy2IxSiuphGxzgQT0d6i2QLAKELQCIxshhKz2OKj2WymWUUlQPW0l2Rjx7AvQKYQsAojFy2OZlJ7HZpCSHhK2X+3JqFnQdUiUgbAFANEYN27bmCvL1dmazSUkOCVtJUnwYfby+mz0ZeoOwBQDRGDVsU03HzWWS0hwWtpKqshz2ZOgNwhYARGPEsK2tyicXp4VsHinNoWEbEeZLq/ua2JOiJwhbABCN0cJ23epWiokMZLNIDQ4NW0lBbjJ7YvQEYQsAojFa2JYUpLMZpBaHh62/jyt1tFSxJ0cvELYAIBojha30uKn02CmXQWpxeNhK0lOi2ROkFwhbABCNkcI2Kz2OzR41CRG2bs6Lqb66kD1JeoCwBQDRGCVsm+pLyNN9GZs9ahIibCVx0UG0fk07e7K0DmELAKIxQthuGuiixLhQNnPUJkzYSsqKMtgTpnUIWwAQjRHCtrIsh80aRxAqbEOCvKi3q449aVqGsAUA0eg9bFf3NlFEqC+bNY4gVNhKcjIT2BOnZQhbABCN3sO2ICeZzRhHES5svT1XUEtDGXvytAphCwCi0XPYdrRUkr+PC5sxjiJc2EqSE8Lpkw097EnUIoQtAIhGz2GblhzFZosjCRm2kuryXPYkapF12AIAiEZPYVtXXUCuzovZXHEkYcM2KtyP1qxsZk+m1mwrymALOACACLanxbJ1l9YM9LdTbFQQmymOJmzYSgrzUtkTqjXWLdv9f/sT7XZbphl7P3qPTn7tqzY3puTUBefT8LtvsJ8xsmM3XCefnxNXX8n+XAuO3zh6DMevuoL9uZENv/u6XPat7wXJya9dYrpX3mc/I6p9L/7Dsv96admWmho2XJaIQOiwDfBzo862avakaolWx2yHMhPo8AP3WPZdujlH3n6VTp99tvzvo7d8j3ZEB7GfNarDP/mxfG6O3Hk7+3Mt0MMxKEEa45TOiXw/fO5zNPLGSzLpv+Xzddcd8jbcZ0WktzHb3s46Cgn0ZLNEBEKHrSQjNYY9sVqixbDlgnZz/+gbvobfe4NOn4PA5SBs9YkLWvPPtBq4egvbnMx4NkNEIXzYursuoYaaIvbkaoXWwnYoSwraey37vO/F52jzuFdpDr/3JgKXgbDVn6mC1mxC4CZHTdhGNHoK2+aGUvL2WM5miCiED1tJfEwwbVjbwZ5kLdBS2M4kaM1GA/cceTsE7iiErb7MJGjNtBa4egnbj9d3U1J8GJsdItFE2ErKizPZE60FWgnboaxE26B9afKgNUPg2kLY6seEoH1z8qA1G3nz5bHA/ZHYgauXsK0qz2UzQzSaCduwYG/q625gT7botBC2ctA+OLugNRt+H4FrhrDVh4lB+zK7Hcc2cH8obODqIWz7+5opMsyPzQzRaCZsJbmmQOBOuOhED1s+aGfXbS8H7rkIXISt9tkE7RlnzCpozeTANX1WPo+CBq4ewrYwL4XNChFpKmx9vJyotamcPekiEzlsh7KloL3Psn9y0M5xfHz4/bcMH7gIW22zR9CaTQjclGh2O0fReth2tlZRgK8rmxUi0lTYSlISI9gTLzJRw3Zi0D4/56A1M3rgImy1y55BayZy4Go9bDNSo9mMEJXmwlZSU5nHnnxRiRi2E4L25fkHrdlo4J4r/16jBS7CVpuUCFqzkbesAvducQJXy2FbX1NEbi5L2HwQlSbDNjoigNauamEvgohEC9uh7CQ6/GNlgtZs+D/GDFyErfZMCFpTOHLbzcfIW69YBe6dQgSuVsN2/ZoOiosOZrNBZJoMW0lxvnYKh0hhywdtJ7vtfBkxcBG22jIxaF9ht7MH0QJXq2FbVpzJZoLoNBu2Qf7u1NVew14M0YgStmoGrZkcuF80TuAibLXDJmjPPFPRoDWTA9f0XfL5lQI31XGBq8Ww7euqp9AgLzYTRKfZsJVkamRZKBHCdihHCtr7Lfux7+UXaPM6ZYPWbPg/bxsmcBG22uCIoDWbGLiOef+7FsM2NyuBzQIt0HTYergtpca6YvaiiMTRYevIoDUzSuAibMXnyKA1EyFwtRa2rY1l5OPpxGaBFmg6bCUJsSG0UeXgmC1Hhq0ctA9ZBe0r6get2fAHUuB+Ud4PvQaukcK2dvMa8ty5md7cu52e3r+H/jmyk/63exvFDW2igU197GccTYSgNZOWq7QE7j13qR64WgrbT0ykxz65DNAKzYetpKI0m71AonBU2A7lJNsE7YgDg9ZM74Gr97DdaApR151b6NrjR8lUqiZ13qlT9OsDw3Igj/8djjIhaE1hx22nJkcGrpbCtroij637tUQXYRtuCrBVPY3sRRKBI8KWC9pP13Wx26pNz4Gr57At3jJANx07zIbrZM4+fZpeG94hh7T171KbTdB+XoygNZMD17RP8jmXAjdNncDVStiuWdlCUeH+bN2vJboIW0l+dhJ7oUSgdtgO5UpB+4DlO+WgHRAjaM2GP3iHTp+nv8DVa9i6mFqz35ymNTuV3xzYS4WDAzbfoxbroD39+c8LFbRmw6Z9kvZNPu8qBa5WwrYoP5Wt87VGN2Hr6+1Mbc0V7MVyNDXDdmLQ/lO4oDXTY+DqMWzdTUF70amTbIjOxqMH91HDp+p2K48PWinUuO1EMDFwlX3aQgth29VWTYF+bmydrzW6CVtJqqnwcBfM0dQKWzloH7YK2lfFDVqz4f/qK3D1FrZlW9bJ46/mwJyvJ/fvZb9TCVoKWrPhd6wC915lA1cLYZtpauFzdb0W6SpsXZwWUm1VPnvRHEmNsB3KTdFc0JrtNQXuqfPOk/db64Grp7A9dNcd9IuDI2xoztWZdJr8dnzKfq89TQhaU4hx24lo+J3XrAL3R4oFruhh22iqNz1cl7J1vRbpKmwlMZGBtG51K3vxHEXpsOWDtpvdVlR6CVw9he3g3XexgTlf1x87ouiEqYlB+xq7ncjUCFyRw3bDuk75sU6ujtcq3YWtpKQwnb2AjqJk2A7lMUG7XltBayYH7vnaDlw9hW3vffeyYWkPEUMfs989XzZBe5Y2g9ZMDlzTMcjlSQrcdPsGrshhW16SxdbtWqbLsA0O8KCejlr2IjqCUmE7GrQPWn63loPWbO9/39V04OopbBseeIANSnt4aXgn+93zYRu0Z2k6aM1GA/cs+ZhGAzeO3W4uRA3bld0NFBbizdbtWqbLsJVk27FQzpcSYTsxaP+l+aA103Lg6ilsqx98kA1Ke7j16CH2u+dKj0FrZhO499kvcEUN27zsRLZO1zrdhq2n+zJqqi9hL6ba7B22ctA+YhW0r+knaM32/k+bgYuwnRnpmV3uu+diQtC+q5+gNZOOyd6BK2LYtjWVk6+XM1una51uw1aSGBdKmwSYkWvPsB3KS9V90JqNBu758nFqJXARtjPHffdsGSFozYbffd0qcO+ed+CKGLbS45tcXa4Hug5bSWVZDntR1WSvsB3KZ4J2Qw+7rV5oLXARtjNzxYlj7HfPhk3QfkEK2tfZ7fREDlzTscplTArcjLkHrmhhW1uZTy4rFrL1uB7oPmwjQn1pdW8Te3HVYo+wNWLQmsmBe4E2AhdhOzM/ODK/MVsjBq2ZvQJXpLBdu7qVoiMD2DpcL3QftpKC3GT2AqtlvmE7GrSjFaDESEFrtvd//9ZE4OopbGsUDNtn9u1mv3smbIP2C4YKWrPRwP2CfA6O3C8Fbjy73VRECtti0/dzdbeeGCJs/X1cqKOlkr3IaphP2MpB+1nlJxl5/UXDBa2ZFgJXT2Hbef99bFDag/eOzex3TwdBO2b43/MLXFHCtru9hoIC3Nm6W08MEbaStOQo9kKrYa5hO5SfhqAdZ++HYgeunsJ24z13s0E5XxefPEH9H69kv3sqE4LWFDbcdkZiG7j3zCpwRQnbrPQ4ts7WG8OEravzYqqrLmAvttKsw1Z6GbpUyKez27S/R+6+0/I5BO2Y0cC9QD4vx266gfa+/xZ7Dh3h6O23yvulh7A9aDq3/yotpgerq+0qKjeDPXdT2fvhe6Y/rr4r79do0L7B7rsRSefCHLhH77iN9i79L3sOx5POqfQZiaPCtqmuhDzdlrF1tt4YJmwlsVFBNNDfzl50JW2tKrAU6rnY/+yf2d9rZNYVhYhOfONSdr+14Ph132KPSRTStef228jmez8MZSWwv1dJ0mOZ0uOZXF2tR4YKW0lpUQZ74RW1pt3yfNxsHfr5T/jfCbTvub+y50wE0nqk3D5rwaFf/JQ9JhHs/8sf2X2GXvnccOdsWmeeSVu6G9jfqaSK0my2jtYrw4VtSKAn9XbWsRdfSVJh3laaJXcpz1h1Ifu7YMzWuhK554A9fw6yzRF/0NnZtopcy/F8ajrHr63qpqs//njObtm4gYpaam3O06yZ9oPbVxgj3w/cuZvEtvJchwTtqt5GCg/1YetovTJc2EpyMmc/TR7A6Fx3bqGzT59mJz1N5Y4jB6nl0372d4Ix5ecksXWznhkybL09llNzQylbCABgclJo/ubAXjZUx7v0xHHymeMjPqBf7c2V5OfjwtbNembIsJUkxYfTxzp9pzCA0jo+WS23dJ/cv5fuOnKArj5+jL539DA9fGgfvTS8gzK2blB0gXjQLukxTK5O1jvDhq2kqjyXLQwAAGB/dVUF5Oq0iK2P9c7QYRsZ5kf9fc1soQAAAPsZ6G+j2KhAti42AkOHraQwL4UtGAAAYD8lhelsHWwUhg/bAF9X6mytYgsHAADMX09nLQUHerJ1sFEYPmwlGanRbAEBAID5y86IZ+teI0HYmri7LKH6miK2kAAAwNw115eSl8dytu41EoTtZ+Kig2n9mg62sAAAwOxJj1cmxYexda7RIGytlBVnsgUGAABmr6osh61rjQhhayU0yIv6uurZQgMAADO3uq+JIsN82brWiBC24+Q6YKkpAAC9KchNYetYo0LYjuPj6UStjWVs4QEAgOl1tFaRv68rW8caFcKWkZIYQZ9s6GELEQAATC09JZqtW40MYTuJ6oo8thABAMDk6qsLyc1lMVuvGhnCdhJREf60ZmULW5gAAGCi9WvaKS46iK1TjQ5hOwVpkXl0JwMATE+qKwtyk9m6FBC204qJDKDayny2cAEAwGjXMVq0U0PYzoCL00JKTYqktuYKtqABABiRNOtYmgyFMdrpIWxnwdfbmfKyk2hlTwNb8AAAjEB6YYX0HC0e75k5hO0chIf4UEVJFm1c18kWRAAAPZLedSy9ghFvhpo9hO08JMSGUGNtMVsoAQD0RFq9B4sKzB3Cdp483JZSZlosdbXXsAUUAEDLpIXfpfVosUze/CBs7STQ352K8lNpzSo8mwsA2jfQ30YlhekUHOjJ1nkwOwhbO4uO8KcavH0KADSsrqqAYqMC2ToO5gZhqxDp/cqtjeVsQQYAEFF7cyWlJUeRq9Mitl6DuUPYKsjHy4lysxKprxtr5AKAuFb1NlJ+ThL5+biwdRnMH8JWBaHBXlRWnEkb1nawBR0AwBE2DXRRZWk2hYf6sHUX2A/CVkXxMcHUUFPEFnoAADU11ZVQYlwoW1eB/SFsVebusoQyUmOos7WKvQEAAJTU3V5DWelx5Om2jK2jQBkIWwcJ8HWjwrwU6l/ZzN4QAAD2tHZ1KxUXpFFQgDtbJ4GyELYOFhnuR1XluVjKDwAUI61cFh0ZwNZBoA6ErSCSE8KppaGMvVEAAOairalcXrHMZcVCtt4B9SBsBeLtsUJesL63s469cQAAZmJldwPlZSeSr5czW9eA+hC2AgoJ9KTSogwa6G9nbyQAAM6GdZ1UXpJFYSHebN0CjoOwFVhsdBDVVxeyNxUAgDVpBTJpJTKuLgHHQ9gKzs15MaWnRFNHSyV7gwGAsXW1Vcsrj3m4LmXrEBADwlYj/H1cqCA3mVb3NrE3HAAYy5qVLfJKY4F+bmydAWJB2GpMRKgvVZbl0KaBbvYGBAB9+2RDL1VX5FFUhD9bR4CYELYalRQfRs31JezNCAD61NpYJq8oxtUJIDaErYZ5uS+n7Iw46umoZW9MANCHvq56ys1KIB9PJ7YuAPEhbHUgOMCDSgrTad3qNvZGBQBtWr+mQ14xLDTIi733QTsQtjoSExlItVUF7E0LANpSX1NEcdHB7L0O2oOw1RkXp0WUlhxJ7c0V7A0MAGKTVgTLSI2WVwjj7nHQJoStTvl5O1N+ThKt6mlkb2gAEEt/X7O8EliAryt7T4O2IWx1LjzEhypKs2njuk72BgcAx/p4fbe88ldkmB97D4M+IGwNIiE2lBrritmbHQAco7mhlJLiw9l7FvQFYWsgnm7LKCs9lrrba9gbHwDUIa3sJa3w5e2xnL1XQX8QtgYU5O9OxQVptHZVK1sRAIAypJW8pBW9pJW9uHsT9Atha2DREQFUU5nPVgoAYF911QUUGxXE3ougfwhbw1sov/6ttamcrSAAYH6kFbvSkqPI1Xkxc/+BUSBsQebr5UR5WYm0sruBrTAAYHakFbqklbqkFbu4ew6MBWELNsKCvam8JIs2rO1gKxAAmNqmgS55ZS5phS7uHgNjQtgCKz4mhBpqi9jKBAB4TfUllBgXyt5TYGwIW5iUu+sSykiNoa62arZiAYBR0spbWelx5Om+jL2XABC2MK1APzcqykulNStb2IoGwKjWrW6VV9ySVt7i7h0AM4QtzFhUuD9VV+TSJxt62IoHwEhqq/Lllba4ewVgPIQtzFpyQji1NJaxFRCA3rU1V1BqUiS5OC1k7w8ADsIW5sTbcwXlZCZQX1c9WyEB6I20glZ+dhL5ejuz9wTAVBC2MC+hQV5UVpRJ69e0sxUUgNZJK2ZVlGbJK2hx9wDATCBswS7iooOovqaQrawAtEpaKSshNoQt8wCzgbAFu3FzWUzpKdHU0VrFVlwAWtHVXkOZabHk4baULesAs4WwBbvz93WlwtwU6u9rYisyAFGtXdVCxflp8spYXNkGmCuELSgmMsyPqspy6OP13WzFBiCSmoo8eSUsriwDzBfCFhSXFB9GzQ2lbAUH4GjSilfSyldc2QWwF4QtqMLLYzllZ8RTT2cdW+EBqK2vu55ysxLJx8uJLbMA9oSwBVUFB3pSaWE6DfS3sRUggNKkFa3KizPlFa64MgqgBIQtOERsVCDVVRWwlSGAUhpqiig+JpgtkwBKQtiCw7g6L6K05Chqb6lkK0YAe+lsq5ZXsJJWsuLKIoDSELbgcH4+LpSfk0yrehvZihJgrvpXNlNhXioF+LmxZQ9ALQhbEEZEqA9VlmbTpoEutuIEmClpZarq8lyKCvdjyxqA2hC2IJzEuFBqqithK1GA6bQ0lMkrU3FlC8BRELYgJE/3ZZSVHkfdHTVshQowXm9XnbwSlbQiFVemABwJYQtCCwrwoOKCNFq7upWtYAGkFadKizIoJMiLLUMAIkDYgibERAZQbWU+W9mCcdVXF8orTnFlBkAkCFvQDJcVCyk1KZLamirYiheMo6OlSl5hys15MVtWAESDsAXN8fV2przsRFrZ3cBWxKBfq/uaqCA3mfx9XNmyASAqhC1oljQRRlpVqK25AgyguiJPfiabKwsAokPYAgAAKAxhCwAAoDCELQAAgMIQtgAAAApD2AIAACgMYQsAAKAwhC0AAIDCELYAAACK+oj+H1uATMgBRYWEAAAAAElFTkSuQmCC\" data-image-state=\"image-loaded\" width=\"238\" height=\"237\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.083px 7.91667px; transform-origin: 231.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to evaluate the complete Figure validation defined in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/spec-v4.1.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpecification\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.25px 7.91667px; transform-origin: 113.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.05px 7.91667px; transform-origin: 381.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u0026lt;= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.   4) Pathological cases of Segments crossing Wall region between Hole Vertices or from figure vertices on Hole edges is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.333px 7.91667px; transform-origin: 175.333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValid=check_figureSP(hxy, pxy, mseg, epsilon, npxy)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.65px 7.91667px; transform-origin: 97.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCrossing Segments appears in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1720\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody 1720\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242.167px 7.91667px; transform-origin: 242.167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.883px 7.91667px; transform-origin: 375.883px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://poses.live/register\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRegister Team\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 7.91667px; transform-origin: 42.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Anyone can select \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://poses.live/problems\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblems Page\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.35px 7.91667px; transform-origin: 256.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and then click problem numbers to see the puzzles and to download problem files.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function valid=check_figureSP(hxy,pxy,mseg,epsilon,npxy)\r\n% hxy hole vertices in order of connection. Last row repeats first for use in inpolygon\r\n% pxy figure original vertices used for initial segment length calculations\r\n% mseg is paired list of connected vertices\r\n% epsilon is allowed stretchiness of segment. hxy,pxy,npxy are all integer\r\n% npxy is figure final vertices used for scoring and Validation\r\n valid=0;\r\n nseg=size(mseg,1);\r\n msegMM=calc_msegMM(pxy,mseg,epsilon,nseg); %Create Min and Max segment integer values\r\n %hplot(hxy,pxy,mseg,size(mseg,1),1);\r\n %hplot3(hxy,npxy,mseg,size(mseg,1),3,segMM);\r\n \r\n%Confirm all final vertices of npxy are in hxy polygon\r\n[in] = inpolygon(npxy(:,1),npxy(:,2),hxy(:,1),hxy(:,2)); % inside or on edge\r\n%check if all vertices are in\r\n\r\n%Confirm all segments are of valid length squared\r\n for i=1:nseg\r\n  nsegL2=0; %calc length squared of segment\r\n  %Check if nsegL2\u003cMin or nsegL2\u003eMax  Min=msegMM(i,1) and Max=msegMM(i,2)\r\n end\r\n \r\n%Confirm all figure segments do not cross hole segments\r\n%Segment/Hole Vertices may touch other vertices and segments\r\n%Intersecting Segments was addressed in Cody 1720\r\n%https://www.mathworks.com/matlabcentral/cody/problems/1720\r\n%A Robust/Fast solution for 1720 was created on 7/18/21 of size 117\r\n \r\n valid=check_intersecting_segments(hxy,mseg,nseg,npxy);\r\n if valid==0,return;end\r\n \r\n valid=check_segments_inpoly(hxy,mseg,npxy);\r\nend % check_figureSP\r\n\r\nfunction valid=check_segments_inpoly(hxy,mseg,npxy)\r\n%Verify whole of segments are within the hole\r\n%Method: Test point along segment at distance \u003c=0.5 from segment start point\r\n valid=0;\r\n dpxy=[]; % start point for each segment\r\n %intra-segment create a point a small delta from starting point; \r\n %mid-point not sufficient\r\n dxdy=[];\r\n dxdyabsmax=[];  % Note: max has a new form of max(m,[],2) to get row max values\r\n dpxy=dpxy+dxdy./dxdyabsmax;\r\n \r\n [in] = inpolygon(dpxy(:,1),dpxy(:,2),hxy(:,1),hxy(:,2)); % inside or on edge\r\n if nnz(in==0),return;end  %nnz is fastest check of a vector all condition\r\n \r\n valid=1;\r\nend %check_segments_inpoly\r\n\r\nfunction valid=check_intersecting_segments(hxy,mseg,nseg,npxy)\r\n%Confirm no figure segments cross hole segments; \r\n % Allowed: \r\n % a) Overlaying segments. \r\n % b) Segments touching hole vertices.\r\n % c) Figure vertices touching hole segments\r\n \r\n valid=0;\r\n nhxy=size(hxy,1)-1;\r\n \r\n for i=1:nseg\r\n  A=[]; % npxy points defined by mseg   A=[a1 a2;a3 a4]\r\n  for j=1:nhxy  %1-2,2-3, end-1 to end  thus why nhxy is 1 less than rows\r\n   B=[]; % hxy points    B=[b1 b2;b3 b4]\r\n   if intersecting(A,B), return;end % intersect detected thus fail\r\n  end\r\n end\r\n \r\n valid=1;\r\nend % check_intersecting_segments\r\n\r\nfunction tf=intersecting(A,B) %\r\n%Correct full solution requires two cross product checks which can be implemented using det\r\n%Segment A [A1;A2],  Segment B [B1;B2]\r\n% Points A1=[a1,a2] A2=[a3,a4] B1=[b1 b2] B2=[b3 b4]  All data in z=0 plane\r\n%p0= B2A1 x B2B1 is det([B2A1;B2B1]) where B2A1 = B2-A1= [b3-a1 b4-a2], B2B1=B2-B1=[b3-b1 b4-b2]\r\n%p1= B2A2 x B2B1 is det([B2A2;B2B1]) where B2A2 = B2-A2= [b3-a3 b4-a4], B2B1=B2-B1=[b3-b1 b4-b2]\r\n%p2= A2B1 x A2A1 is det([A2B1;A2A1]) where A2B1 = A2-B1= [a3-b1 a4-b2], A2A1=A2-A1=[a3-a1 a4-a2]\r\n%p3= A2B2 x A2A1 is det([A2B2;A2A1]) where A2B2 = A2-B2= [a3-b3 a4-b4], A2A1=A2-A1=[a3-a1 a4-a2]\r\n%visualization https://www.desmos.com/calculator/0wr2rfkjbk\r\n%source https://stackoverflow.com/questions/3838329/how-can-i-check-if-two-segments-intersect\r\n% by BenMan95 in ghastly Python not using det or matlab array vectors\r\n%https://www.mathworks.com/matlabcentral/cody/problems/1720\r\n%  Robust Fast solution of size 117 created on 7/18/21 for 1720\r\n%\r\n% Both cross product pair multiplications must be negative for an intersection to occur\r\n% p0p1\u003c0 \u0026\u0026 p2p3\u003c0 for non-endpoint segments intersection. For End point intersection change \u003c to \u003c=\r\n\r\ntf=0;\r\nend % intersecting\r\n\r\n\r\nfunction msegMM=calc_msegMM(pxy,mseg,epsilon,nseg)\r\n%determine Min and Max integer value of allowed length squared for each segment\r\n%abs(Lsqr(npxy,seg(i))/Lsqr(pxy,seg(i))-1)\u003c= epsilon/1000000.\r\n%mseg has indices of connected vertices [nseg,2].  The nseg may exceed number of vertices.\r\n msegMM=zeros(nseg,2);\r\n for i=1:nseg\r\n  Lseg=0; % sum((pxy(mseg(i,1),:)-pxy(mseg(i,2),:)).^2)\r\n  delta=0; % epsilon*Lseg/1000000 and a little tweak\r\n  msegMM(i,:)=[-delta delta]+Lseg;\r\n end\r\nend % calc_msegMM\r\n\r\n%These routines can be used to visualize the data\r\n\r\n% function hplot(vxy,qxy,mseg,Lmseg,id)\r\n% %Need check of segment crossing a hole segment but ignore endpoint\r\n%  [in] = inpolygon(qxy(:,1),qxy(:,2),vxy(:,1),vxy(:,2)); % inside or on edge\r\n%  figure(id)\r\n%   plot(vxy(:,1),vxy(:,2),'k.-') % hole polygon\r\n%   hold on\r\n%   plot(qxy(in,1),qxy(in,2),'b*') % points inside\r\n%   plot(qxy(~in,1),qxy(~in,2),'ro') % points outside\r\n%   for i=1:size(qxy,1)%length(xq)\r\n%    text(qxy(i,1)+.75,qxy(i,2)-1.5,num2str(i),'FontSize',12);\r\n%   end\r\n%   \r\n%   for i=1:Lmseg\r\n%    if in(mseg(i,1))+in(mseg(i,2))\u003c2\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'r-') % segment to OOB pt\r\n%    else\r\n%     plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'b-')\r\n%    end\r\n%    text(sum(qxy(mseg(i,:),1))/2,sum(qxy(mseg(i,:),2))/2,num2str(i),'Color','b');\r\n%   end\r\n%   \r\n%   %o+*.x_|sd^v\u003e\u003cph\r\n%   %colors ymcrgbwk\r\n%    \r\n%   axis tight\r\n%   axis ij\r\n%   hold off  \r\n% end % hplot\r\n\r\n% function hplot3(vxy,qxy,mseg,Lmseg,id,segMM)\r\n%  segMNM=[segMM(:,1) segMM(:,1)+segMM(:,2) segMM(:,2)];\r\n%  [in] = inpolygon(qxy(:,1),qxy(:,2),vxy(:,1),vxy(:,2)); % inside or on edge\r\n%  figure(id)\r\n%   plot(vxy(:,1),vxy(:,2),'k.-') % hole polygon\r\n%   hold on\r\n%   plot(qxy(in,1),qxy(in,2),'b*') % points inside\r\n%   plot(qxy(~in,1),qxy(~in,2),'ro') % points outside\r\n%   for i=1:size(qxy,1) %length(xq)\r\n%    text(qxy(i,1)+.75,qxy(i,2)-1.5,num2str(i));\r\n%   end\r\n%   \r\n%   for i=1:Lmseg\r\n%    d2seg=(qxy(mseg(i,1),1)-qxy(mseg(i,2),1))^2+(qxy(mseg(i,1),2)-qxy(mseg(i,2),2))^2;\r\n%    if d2seg\u003csegMNM(i,1)\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'b-') % segment too short\r\n%    elseif d2seg\u003esegMNM(i,3)\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'r-') % segment too long\r\n%    else\r\n%     plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'g-') \r\n%    end\r\n%    text(sum(qxy(mseg(i,:),1))/2,sum(qxy(mseg(i,:),2))/2,num2str(i),'Color','b');\r\n%   end\r\n%   \r\n%   %o+*.x_|sd^v\u003e\u003cph\r\n%   %colors ymcrgbwk\r\n%   \r\n%   axis tight\r\n%   axis ij\r\n%   hold off\r\n% end % hplot3\r\n%","test_suite":"%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=pxy;\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0+10\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0.001    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0; %non-integer npxy\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16+1    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[15     0\r\n    35    20\r\n    20    44\r\n     0    24\r\n    15     0];\r\npxy=[0    20\r\n    20     0\r\n    20    40\r\n    40    20\r\n    49    45];\r\nmseg=[1     2\r\n     1     3\r\n     2     4\r\n     3     4\r\n     3     5\r\n     4     5];\r\nepsilon=1250;\r\nnpxy=[20    44\r\n     0    24\r\n    35    20\r\n    15     0\r\n     6    25];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n\r\n%%\r\n% Problem 6 shifted up7,left10, 1 seg fail\r\nepsilon=150000;\r\nhxy=[164   164\r\n   121   189\r\n    71   189\r\n    28   164\r\n     3   121\r\n     3    71\r\n    28    28\r\n    71     3\r\n   121     3\r\n   164    28\r\n   189    71\r\n    96    96\r\n   189   121\r\n   164   164];\r\npxy=[36    86\r\n    36   141\r\n    36   156\r\n    41   156\r\n    46   131\r\n    51    56\r\n    56   116\r\n    56   141\r\n    66   116\r\n    71    81\r\n    71    96\r\n    71   131\r\n    71   156\r\n    86    81\r\n    86    96\r\n    86   131\r\n    86   141\r\n    86   156\r\n    91   116\r\n    96    36\r\n   101   116\r\n   106    81\r\n   106    96\r\n   106   131\r\n   106   141\r\n   106   156\r\n   121    81\r\n   121    96\r\n   121   131\r\n   121   156\r\n   126   116\r\n   136   116\r\n   136   141\r\n   141    56\r\n   146   131\r\n   151   156\r\n   156    86\r\n   156   141\r\n   156   156];\r\nmseg=[2     3\r\n     3     4\r\n     4     8\r\n     8     2\r\n     2     1\r\n     1     6\r\n     6    20\r\n    20    34\r\n    34    37\r\n    37    38\r\n    38    33\r\n    33    36\r\n    36    39\r\n    39    38\r\n    33    30\r\n    30    26\r\n    26    25\r\n    25    33\r\n     8    17\r\n    17    18\r\n    18    13\r\n    13     8\r\n    17    25\r\n    10    11\r\n    11    15\r\n    15    14\r\n    14    10\r\n    22    23\r\n    23    28\r\n    28    27\r\n    27    22\r\n     6    10\r\n    10     1\r\n    34    27\r\n    27    37\r\n     5     7\r\n     7     9\r\n     9    12\r\n    12    16\r\n    16    19\r\n    19    21\r\n    21    24\r\n    24    29\r\n    29    31\r\n    31    32\r\n    32    35\r\n    15    19\r\n    23    21];\r\nnpxy=[26    79\r\n    26   134\r\n    26   149\r\n    31   149\r\n    36   124\r\n    41    49\r\n    46   109\r\n    46   134\r\n    56   109\r\n    61    74\r\n    61    89\r\n    61   124\r\n    61   149\r\n    76    74\r\n    76    89\r\n    76   124\r\n    76   134\r\n    76   149\r\n    81   109\r\n    86    29\r\n    91   109\r\n    96    74\r\n    96    89\r\n    96   124\r\n    96   134\r\n    96   149\r\n   111    74\r\n   111    89\r\n   111   124\r\n   111   149\r\n   116   109\r\n   126   109\r\n   126   134\r\n   131    49\r\n   136   124\r\n   141   149\r\n   146    79\r\n   146   134\r\n   146   149];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\n%problem 6 with rotate/shift, 1 seg fail\r\nepsilon=150000;\r\nhxy=[164   164\r\n   121   189\r\n    71   189\r\n    28   164\r\n     3   121\r\n     3    71\r\n    28    28\r\n    71     3\r\n   121     3\r\n   164    28\r\n   189    71\r\n    96    96\r\n   189   121\r\n   164   164];\r\npxy=[36    86\r\n    36   141\r\n    36   156\r\n    41   156\r\n    46   131\r\n    51    56\r\n    56   116\r\n    56   141\r\n    66   116\r\n    71    81\r\n    71    96\r\n    71   131\r\n    71   156\r\n    86    81\r\n    86    96\r\n    86   131\r\n    86   141\r\n    86   156\r\n    91   116\r\n    96    36\r\n   101   116\r\n   106    81\r\n   106    96\r\n   106   131\r\n   106   141\r\n   106   156\r\n   121    81\r\n   121    96\r\n   121   131\r\n   121   156\r\n   126   116\r\n   136   116\r\n   136   141\r\n   141    56\r\n   146   131\r\n   151   156\r\n   156    86\r\n   156   141\r\n   156   156];\r\nmseg=[2     3\r\n     3     4\r\n     4     8\r\n     8     2\r\n     2     1\r\n     1     6\r\n     6    20\r\n    20    34\r\n    34    37\r\n    37    38\r\n    38    33\r\n    33    36\r\n    36    39\r\n    39    38\r\n    33    30\r\n    30    26\r\n    26    25\r\n    25    33\r\n     8    17\r\n    17    18\r\n    18    13\r\n    13     8\r\n    17    25\r\n    10    11\r\n    11    15\r\n    15    14\r\n    14    10\r\n    22    23\r\n    23    28\r\n    28    27\r\n    27    22\r\n     6    10\r\n    10     1\r\n    34    27\r\n    27    37\r\n     5     7\r\n     7     9\r\n     9    12\r\n    12    16\r\n    16    19\r\n    19    21\r\n    21    24\r\n    24    29\r\n    29    31\r\n    31    32\r\n    32    35\r\n    15    19\r\n    23    21];\r\nnpxy=[53   156\r\n   108   156\r\n   123   156\r\n   123   151\r\n    98   146\r\n    23   141\r\n    83   136\r\n   108   136\r\n    83   126\r\n    48   121\r\n    63   121\r\n    98   121\r\n   123   121\r\n    48   106\r\n    63   106\r\n    98   106\r\n   108   106\r\n   123   106\r\n    83   101\r\n     3    96\r\n    83    91\r\n    48    86\r\n    63    86\r\n    98    86\r\n   108    86\r\n   123    86\r\n    48    71\r\n    63    71\r\n    98    71\r\n   123    71\r\n    83    66\r\n    83    56\r\n   108    56\r\n    23    51\r\n    98    46\r\n   123    41\r\n    53    36\r\n   108    36\r\n   123    36];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nepsilon=100000; %vertext to vertex across wall\r\nhxy=[0 0;0 2;2 2;1 1;2 0;0 0];\r\npxy=[0 0;0 2;2 2;2 0];\r\nmseg=[1 2;2 3;3 4;4 1];\r\nnpxy=[0 0;0 2;2 2;2 0];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nepsilon=100000; % mid seg connects across wall\r\nhxy=[0 0;0 4;4 4;2 2;4 0;0 0];\r\npxy=[0 0;0 4;3 3;3 1];\r\nmseg=[1 2;2 3;3 4;4 1];\r\nnpxy=[0 0;0 4;3 3;3 1];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nepsilon=100000; %mid seg intersect node\r\nhxy=[0 0;0 4;4 4;1 2;4 2;1 1;4 0;0 0];\r\npxy=[0 0;0 4;4 4;4 0];\r\nmseg=[1 2;2 3;3 4;4 1];\r\nnpxy=[0 0;0 4;4 4;4 0];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-19T18:59:14.000Z","updated_at":"2021-07-19T19:33:01.000Z","published_at":"2021-07-19T19:33:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.icfpconference.org/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eICFP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e held its annual 3-day contest in July 2021 with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eHole-In-Wall\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Contest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/spec-v4.1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpecification\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe contest folds the figure in Red to fit within the hole shown in light grey \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"237\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"238\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to evaluate the complete Figure validation defined in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/spec-v4.1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpecification\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u0026lt;= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.   4) Pathological cases of Segments crossing Wall region between Hole Vertices or from figure vertices on Hole edges is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValid=check_figureSP(hxy, pxy, mseg, epsilon, npxy)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCrossing Segments appears in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1720\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody 1720\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://poses.live/register\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRegister Team\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Anyone can select \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://poses.live/problems\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblems Page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and then click problem numbers to see the puzzles and to download problem 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Sequences 110: Integration of the Sum of a Recursive Trigonometric Function","description":"A trigonometric function, , is defined as follows:\r\n                ,  in radians\r\nApplying  recursively we define another function , for integer :\r\n                \r\nWe then define  as the sum of value of  from  to :\r\n                \r\nFinally, we are asked to evaluate the integral of  with respect to , over the real range :\r\n                \r\nFor example for , , , we have:\r\n  \u003e\u003e a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\r\n       a = 7.05797686912156\r\nPlease present the final output rounded-off to 6 decimal places. Therefore the final answer is .\r\n-------------------------\r\nNOTE: There are a number of ways to do numerical Integration in Matlab.  Just make sure that the output would be accurate within 6 decimal places of the value obtained using the integral function shown above.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 507px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 462.578125px 253.5px; transform-origin: 462.578125px 253.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA trigonometric function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"19\" style=\"width: 137.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in radians\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eApplying \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e recursively we define another function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, for integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 51px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 25.5px; text-align: left; transform-origin: 384px 25.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"166.5\" height=\"51\" style=\"width: 166.5px; height: 51px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe then define \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"19\" style=\"width: 44px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the sum of value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"46\" style=\"width: 129.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFinally, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ewe are asked to evaluate the integral of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, over the real range \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-21px\"\u003e\u003cimg 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width=\"204\" height=\"48\" style=\"width: 204px; height: 48px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFUAAAAoCAYAAACPSbZFAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAVaADAAQAAAABAAAAKAAAAAAM7AvNAAADQklEQVRoBe2YXYhNURTHr2FQXnyNj8jDiEk+nwilaJoHkrxQXowkHqQkUhJ5kMRISeJhUogX8eAj+QpF3ijEUIwUaZihkW9+f/aq0+Xee+69Z9x7x1r1m7XPXvuus/b/nL3PJpVycwVcAVfAFXAFXAFXwBVwBVwBV8AVcAVcAVfAFchLgR5ZRtcRq4daOA3XwGwQjeUwAHZAB3Qnq2Iyw6AGsmn0krjIaRLzAXyFH4GPeAkpU/wFWGyLOruJjWceR+AT2PyyeY2NZf0YNRb0tPaAJV1MezA8Ab21Z+EVzIOkbBqJ2hLgQgEFNfCb92DzjeOXFnCf1OTITfbSPglXoBq6wmaSNM5kco25lWdxeok6QS/KVrD8TbSXwZrQ9xmvbU99QtvfH5Ztv9Bgxd9Af11g7TABtPy7wnSfRQkkbiXH+Tzy3GDsMdgP4+A+SEDtqe+gEZrhEtRD0XaODPbkVhedrTwT9I6UtTvM90yk72LoWxvpK6q5OSSUsJNiZNKTPgx/XRoxfl/KIRL3NWiuK0IhI/DfQp+2iURsPVnsTV2ZJeMYYvoaWgE6klSaaevRXL/D8FD8htD3OFwX7UaTIfpFlGiZbBWBOfABVFghopby60/JKZ0aVPttXQS7i1ffPusoxvfixzfhOtwBJX4GuayFAYWKWqqvv+Y0EfSGqvaNINO5VddiPsiGgLaEjCbhMpn2Ui3pKbAOtJ+OCujrOhdGwkFIyu6RKNsWE/c+qi8fG8pgzUOnnS/QDLKG3+7X30f8VfwQnAIbQzOz1RKSUH1hAehfVPZ0FtK2J6YTgD5GbTAb0q2FDo0tZPmn5/oX143c5C3Y/I5Hbnog0n+V9mV4CtUQy54zSok7QctgJ5jp/Gh7peLtsMuCab6SRO1D7R1ggmpuWvJm22lYzHxeK0lLz354lHaVZQ5ey8PiJ2j3TIvbZSWJqlVpRyjNbYlNIvgZeDvNyG9Li+e81H+YaLnXZRip/WQWTM8Qt+5KElU161uxBaL7p/rNtNVpWxxoHaXwlSZq4hqlL/HEb/A/JnRRK+Cp11CjjmLa9KdWQL1lX+ImKmwFOyE8pN1U9lV7ga6AK+AKuAKugCvgCrgC5ajAT9QuCWFBDigLAAAAAElFTkSuQmCC\" width=\"42.5\" height=\"20\" style=\"width: 42.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"20\" style=\"width: 50px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 459.578125px 20px; transform-origin: 459.578125px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 459.578125px 10px; transform-origin: 459.578125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 459.578125px 10px; transform-origin: 459.578125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       a = 7.05797686912156\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85.5\" height=\"18\" style=\"width: 85.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThere are a number of ways to do \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/numerical-integration-and-differentiation.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003enumerical Integration\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in Matlab.  Just make sure that the output would be accurate within 6 decimal places of the value obtained using the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = A(n,x1,x2) \r\n    y = x;\r\nend","test_suite":"%%\r\n[n,x1,x2] = deal(1:10,pi,2*pi);\r\na_correct = [3.065357 5.25927 7.057977 8.618935 10.016842 11.294017 12.477158 13.584381 14.628646 15.619599];\r\nassert(all(abs(arrayfun(@(i) A(i,x1,x2),n)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(12,exp(1),exp(1.5));\r\na_correct = 9.752678;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(15,-2,10);\r\na_correct = 50.909769;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(25,-10*pi,0);\r\na_correct = -267.631308;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(1000,0,1000);\r\na_correct = 61793.524569;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(10000,5,1234);\r\na_correct = 244011.112390;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(123456,10000,12345);\r\na_correct = 1644471.557504;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(1:1000,-pi,20*exp(1));\r\na = arrayfun(@(i) A(i,x1,x2),n);\r\ns = round([sum(a) sum(diff(a,1)) sum(diff(a,2)) sum(diff(a,3))]);\r\ns_correct = [2087798 3114 -35 7];\r\nassert(isequal(s,s_correct))\r\n%%\r\n[n,x1,x2] = deal(randi(15),rand(),100*rand());\r\nt = 'sin(atan(';\r\na_correct = 0;\r\nfor i = 1:n\r\n    a_correct = a_correct + integral(str2num(['@(x)' repmat('sin(atan(',1,i) 'x' repmat('))',1,i)]),x1,x2);\r\nend\r\na_correct = round(a_correct,6);\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\nfiletext = fileread('A.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-23T09:34:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-16T08:49:13.000Z","updated_at":"2023-04-23T09:34:40.000Z","published_at":"2023-04-16T17:57:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA trigonometric function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x) = \\\\sin(\\\\arctan(x))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in radians\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eApplying \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e recursively we define another function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)=\\\\underbrace{\\\\text{T}(\\\\text{T}(\\\\text{T}(...\\\\text{T}(x))))}\\\\\\\\_{\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\text{n times}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe then define \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the sum of value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}(x,n) = \\\\sum_{k=1}^{n} \\\\text{R}(x,k) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFinally, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewe are asked to evaluate the integral of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, over the real range \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[x_1,x_2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=\\\\text{A}(n,x_1,x_2) = \\\\int^{x_2}_{x_1} \\\\text{S}(x,n)\\\\ \\\\mathrm{d}x}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1=\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2=2\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[  \u003e\u003e a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\\n       a = 7.05797686912156]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=7.057977\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThere are a number of ways to do \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/numerical-integration-and-differentiation.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumerical Integration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in Matlab.  Just make sure that the output would be accurate within 6 decimal places of the value obtained using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57983,"title":"Easy Sequences 109: Summation of Derivatives of a Trigonometric Function","description":"A trigonometric function, ,  is defined as follows:\r\n                \r\n                where:     ; and \r\n                                 is in radians.\r\nIn this problem we are asked to evaluate the following summation:\r\n                \r\n                where:     is a real number; \r\n                                 is an integer; \r\n                                 or the -th derivative of  with respect to ; and \r\n                                .\r\nFor example for  and , we have:\r\n  \u003e\u003e  syms x;\r\n  \u003e\u003e  T = (1+2*tan(x)-tan(x)^2) / (1+tan(x)^2);\r\n  \u003e\u003e  S = T/2^0 + diff(T)/2^1 + diff(T,2)/2^2;\r\n  \u003e\u003e  s = vpa(subs(S,x,2))\r\n        s = 0.10315887444431633673347091141408;\r\nPlease present the final output rounded-off to 6 decimal places. Therefore the final answer is .\r\n-------------------------\r\nNOTE: Symbolic toolbox is not available to Cody players. It is possible to do numerical differentiation in Matlab without symbolic toolbox.  Just make sure that the output would be accurate within 6 decimal places of the 'exact' value obtained using syms, as shown above.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 622px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 311px; transform-origin: 407px 311px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA trigonometric function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,  is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19px; text-align: left; transform-origin: 384px 19px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-14px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"133.5\" height=\"38\" style=\"width: 133.5px; height: 38px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                where:     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"152.5\" height=\"20\" style=\"width: 152.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e; and \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is in radians.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIn this problem we are asked to evaluate the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"142.5\" height=\"46\" style=\"width: 142.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                where:    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is a real number; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.5px; text-align: left; transform-origin: 384px 18.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"112.5\" height=\"37\" style=\"width: 112.5px; height: 37px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e or the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th derivative of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e; and \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"20\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAASaADAAQAAAABAAAAJAAAAABLVRfgAAAC1klEQVRoBe2YS6hNURjHL/ciMnAVUiR5DK+MLsnAo8vAo5SBiUJGJgyUZCC5XQolYoaJiUSZkoRSkjCRRySFEgbk/fr9aq9ajrPv3efsW/ece9ZXv/Y6a3177fX997ce+7S1JUsKJAWSAkmBpMBwU2DEcAuon3hG0bYEumAuPIdbcBs+Q8vbPBS4B3+q8I66bmhpm0P0Zko1gULdR9qXtqpKLifX4Rf0wVRoh1nZ7+9cg1B3KLekLSRqRdiTE/3WrF0fhezM8RvW1b1E9xBG5kRppj2BkE1rqvnl3VzNtxnrJjDovfA7Z/CKcz9qq+rXETlUK46lcjnMB9PxKHyCYCso2H4DLoXKBrpuKzCWr5HPs6hcqHgQL1d9xQnpeCi683BUr3DjorZmKt7M4nhUz6A9cI2HaaAICuX81naAdadA9S9DEbuAk+eSsiwr8rACPpPx+QHGtr2Af78uF7OO7KwHTFGnWq2mmCEry1xX1vrgHP+d2XhclzyRV7WinyVmzpGoB6edD6jVzADPKGXNl/a2ZCeemZwZY2AR3IVS5rE9vPkXlJt1/QkimBxOfXez9aGy7HU0HXwBhbLzZrd9BGAs9cyG3NjNHNPbjl/nejVHw8Ysjr7BHu6JrOMw5WbX+QCzsOzO5v317m5rudfd7CQMqq2iN89KsVCb6nzCUO5uCuuufBbyvjQ6adsP/9hAu9sUvB/AGTgAvkXvOQ2bwW3zGOyG9zCQDdXutoCBXYGrsA5+QqUZy3nwb5UNcWOlSB00ev55DC/BjtthMdix54kueAPT4Th46DR4p2IjmuO9BmbJOXADqrSJVHgM8GosiplrW2gJ646fJC7WMyJvF7vQ/oqymRW3R64NUfQF+kLDmAe6PsW3MnH+C8QzQ+jI6eP/MbHN5Mc30OcDmGGNbLWugbuKBtONYw/kHRj93lkNkyBZUiApkBRICiQFkgJJgaRACyvwF8of8w03SG40AAAAAElFTkSuQmCC\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 100px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 50px; transform-origin: 404px 50px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt;  syms x;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt;  T = (1+2*tan(x)-tan(x)^2) / (1+tan(x)^2);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt;  S = T/2^0 + diff(T)/2^1 + diff(T,2)/2^2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt;  s = vpa(subs(S,x,2))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        s = 0.10315887444431633673347091141408;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"83.5\" height=\"18\" style=\"width: 83.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSymbolic toolbox is not available to Cody players. It is possible to do \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.unioviedo.es/compnum/labs/lab07_der_int/lab07_der_int.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003enumerical differentiation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in Matlab without symbolic toolbox.  Just make sure that the output would be accurate within 6 decimal places of the 'exact' value obtained using \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003esyms\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, as shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(x,n)\r\n  s = x;\r\nend","test_suite":"%%\r\nx = 1:10; n = 2;\r\ns_correct = [-1.325444 0.103159 1.239586 -1.134858 -0.29505 1.380427 -0.85387 -0.669756 1.411304 -0.504863];\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 11:20; n = 2*x;\r\ns_correct = [-0.991110 -0.481399 -0.115639 -0.691700 1.142283 1.385650 -1.377653 -1.119743 0.658705  0.078175];\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 25.25; n = 25;\r\ns_correct = 1.945253;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 100; n = 100;\r\ns_correct = -0.386110;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 0.000123; n = 123;\r\ns_correct = 0.000001;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 1234; n = 1:1000;\r\na_correct = [275 250];\r\nassert(isequal([round(sum(S(x,n))) sum(round(S(x,n)))],a_correct))\r\n%%\r\nx = 123456; n = 123456;\r\ns_correct = 0.899338;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 123456789.10111213; n = 123456789;\r\ns_correct = -1.993727;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = rand()*randi(1000); n = randi(10)-1;\r\nTs = { \r\n       @(a) (2*tan(a) - tan(a)^2 + 1)/(tan(a)^2 + 1);\r\n       @(a) (2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2)/(tan(a)^2 + 1) - (2*tan(a)*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1);\r\n       @(a) 2*tan(a)^2 - 4*tan(a) - (4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2)/(tan(a)^2 + 1) + (4*tan(a)^2*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) - (4*tan(a)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - 2;\r\n       @(a) 8*tan(a)*(2*tan(a) - tan(a)^2 + 1) - 12*tan(a)^2 - (16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2)/(tan(a)^2 + 1) + 12*tan(a)*(tan(a)^2 + 1) + (12*tan(a)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - (8*tan(a)^3*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) + (6*tan(a)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - 12;\r\n       @(a) 8*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) - (16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3)/(tan(a)^2 + 1) + 48*tan(a)^2*(tan(a)^2 + 1) - 24*tan(a)^2*(2*tan(a) - tan(a)^2 + 1) - 48*tan(a)*(tan(a)^2 + 1) + 32*tan(a)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 24*(tan(a)^2 + 1)^2 - (24*tan(a)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (32*tan(a)^3*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) + (8*tan(a)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (16*tan(a)^4*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1);\r\n       @(a) 320*tan(a)*(tan(a)^2 + 1)^2 - 160*tan(a)^2*(tan(a)^2 + 1) + 160*tan(a)^3*(tan(a)^2 + 1) - 120*tan(a)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - (272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3)/(tan(a)^2 + 1) + 40*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 64*tan(a)^3*(2*tan(a) - tan(a)^2 + 1) - 80*tan(a)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - 80*(tan(a)^2 + 1)^2 + (80*tan(a)^3*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (80*tan(a)^4*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - (32*tan(a)^5*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) - (40*tan(a)^2*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (10*tan(a)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1);\r\n       @(a) 480*tan(a)^4*(tan(a)^2 + 1) - 960*tan(a)*(tan(a)^2 + 1)^2 - 480*tan(a)^3*(tan(a)^2 + 1) - (64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4)/(tan(a)^2 + 1) + 360*tan(a)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 384*tan(a)^3*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 160*tan(a)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 32*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) + 2640*tan(a)^2*(tan(a)^2 + 1)^2 - 120*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - 160*tan(a)^4*(2*tan(a) - tan(a)^2 + 1) + 480*(tan(a)^2 + 1)^3 - (240*tan(a)^4*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (60*tan(a)^2*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - (192*tan(a)^5*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) + 128*tan(a)^2*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) + (12*tan(a)*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 192*tan(a)*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + (64*tan(a)^6*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) + (160*tan(a)^3*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1);\r\n       @(a) 11424*tan(a)*(tan(a)^2 + 1)^3 - 280*(tan(a)^2 + 1)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 224*(tan(a)^2 + 1)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 1344*tan(a)^4*(tan(a)^2 + 1) + 1344*tan(a)^5*(tan(a)^2 + 1) - 1344*tan(a)^3*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - 1120*tan(a)^4*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 7392*tan(a)^2*(tan(a)^2 + 1)^2 + 17472*tan(a)^3*(tan(a)^2 + 1)^2 - (7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4)/(tan(a)^2 + 1) + 384*tan(a)^5*(2*tan(a) - tan(a)^2 + 1) + 840*tan(a)^2*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 280*tan(a)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 1344*(tan(a)^2 + 1)^3 + (672*tan(a)^5*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (280*tan(a)^3*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) + (448*tan(a)^6*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) + 128*tan(a)*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) - 384*tan(a)^3*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) + 672*tan(a)*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (128*tan(a)^7*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) - (560*tan(a)^4*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (84*tan(a)^2*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) + 896*tan(a)^2*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + (14*tan(a)*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1);\r\n       @(a) 3584*tan(a)^6*(tan(a)^2 + 1) - 30464*tan(a)*(tan(a)^2 + 1)^3 - 3584*tan(a)^5*(tan(a)^2 + 1) - (256*tan(a)^8*(tan(a)^2 + 1) - 256*tan(a)^7*(tan(a)^2 + 1) - 15872*tan(a)*(tan(a)^2 + 1)^4 + 137216*tan(a)^2*(tan(a)^2 + 1)^4 - 49152*tan(a)^3*(tan(a)^2 + 1)^3 + 185856*tan(a)^4*(tan(a)^2 + 1)^3 - 15360*tan(a)^5*(tan(a)^2 + 1)^2 + 31616*tan(a)^6*(tan(a)^2 + 1)^2 + 7936*(tan(a)^2 + 1)^5)/(tan(a)^2 + 1) + 4480*tan(a)^4*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 1680*tan(a)^2*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) + 3072*tan(a)^5*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 448*tan(a)*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) + 128*(tan(a)^2 + 1)^3*(2*tan(a) - tan(a)^2 + 1) + 161280*tan(a)^2*(tan(a)^2 + 1)^3 - 46592*tan(a)^3*(tan(a)^2 + 1)^2 + 102144*tan(a)^4*(tan(a)^2 + 1)^2 - 560*(tan(a)^2 + 1)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 896*tan(a)^6*(2*tan(a) - tan(a)^2 + 1) - 3584*tan(a)^3*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) + 15232*(tan(a)^2 + 1)^4 + 896*(tan(a)^2 + 1)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (1792*tan(a)^6*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (1120*tan(a)^4*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - (1024*tan(a)^7*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - (112*tan(a)^2*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) + 1152*tan(a)^4*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) + (16*tan(a)*(7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) - 640*tan(a)^2*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) + (256*tan(a)^8*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) + (1792*tan(a)^5*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (448*tan(a)^3*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 3584*tan(a)^2*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 1024*tan(a)*(tan(a)^2 + 1)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 3072*tan(a)^3*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 1792*tan(a)*(tan(a)^2 + 1)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2);\r\n       @(a) 1152*(tan(a)^2 + 1)^3*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 571392*tan(a)*(tan(a)^2 + 1)^4 - 9216*tan(a)^6*(tan(a)^2 + 1) + 9216*tan(a)^7*(tan(a)^2 + 1) - 1008*(tan(a)^2 + 1)*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) - 13824*tan(a)^5*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - 8064*tan(a)^3*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 8064*tan(a)^6*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 2688*(tan(a)^2 + 1)^2*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 414720*tan(a)^2*(tan(a)^2 + 1)^3 + 1769472*tan(a)^3*(tan(a)^2 + 1)^3 - 262656*tan(a)^4*(tan(a)^2 + 1)^2 + 552960*tan(a)^5*(tan(a)^2 + 1)^2 - (353792*tan(a)*(tan(a)^2 + 1)^5 - 512*tan(a)^8*(tan(a)^2 + 1) + 512*tan(a)^9*(tan(a)^2 + 1) - 274432*tan(a)^2*(tan(a)^2 + 1)^4 + 1841152*tan(a)^3*(tan(a)^2 + 1)^4 - 371712*tan(a)^4*(tan(a)^2 + 1)^3 + 1304832*tan(a)^5*(tan(a)^2 + 1)^3 - 63232*tan(a)^6*(tan(a)^2 + 1)^2 + 128512*tan(a)^7*(tan(a)^2 + 1)^2 - 15872*(tan(a)^2 + 1)^5)/(tan(a)^2 + 1) + 2048*tan(a)^7*(2*tan(a) - tan(a)^2 + 1) + 13440*tan(a)^4*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) + 3024*tan(a)^2*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) - 39168*(tan(a)^2 + 1)^4 - 672*tan(a)*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4) + (4608*tan(a)^7*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (4032*tan(a)^5*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + (2304*tan(a)^8*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) + (672*tan(a)^3*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) - 512*tan(a)*(tan(a)^2 + 1)^3*(2*tan(a) - tan(a)^2 + 1) - 3072*tan(a)^5*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) - 10752*tan(a)^2*(tan(a)^2 + 1)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) + 4032*tan(a)*(tan(a)^2 + 1)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) + 2048*tan(a)^3*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) - (512*tan(a)^9*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) - (5376*tan(a)^6*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (2016*tan(a)^4*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 4608*tan(a)*(tan(a)^2 + 1)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 13824*tan(a)^3*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (144*tan(a)^2*(7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) + 10368*tan(a)^4*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + (18*tan(a)*(256*tan(a)^8*(tan(a)^2 + 1) - 256*tan(a)^7*(tan(a)^2 + 1) - 15872*tan(a)*(tan(a)^2 + 1)^4 + 137216*tan(a)^2*(tan(a)^2 + 1)^4 - 49152*tan(a)^3*(tan(a)^2 + 1)^3 + 185856*tan(a)^4*(tan(a)^2 + 1)^3 - 15360*tan(a)^5*(tan(a)^2 + 1)^2 + 31616*tan(a)^6*(tan(a)^2 + 1)^2 + 7936*(tan(a)^2 + 1)^5))/(tan(a)^2 + 1);\r\n       @(a) 6720*(tan(a)^2 + 1)^2*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 1428480*tan(a)*(tan(a)^2 + 1)^4 - 23040*tan(a)^7*(tan(a)^2 + 1) + 23040*tan(a)^8*(tan(a)^2 + 1) + 40320*tan(a)^6*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (1024*tan(a)^10*(tan(a)^2 + 1) - 1024*tan(a)^9*(tan(a)^2 + 1) - 707584*tan(a)*(tan(a)^2 + 1)^5 + 9061376*tan(a)^2*(tan(a)^2 + 1)^5 - 3682304*tan(a)^3*(tan(a)^2 + 1)^4 + 21253376*tan(a)^4*(tan(a)^2 + 1)^4 - 2609664*tan(a)^5*(tan(a)^2 + 1)^3 + 8728576*tan(a)^6*(tan(a)^2 + 1)^3 - 257024*tan(a)^7*(tan(a)^2 + 1)^2 + 518656*tan(a)^8*(tan(a)^2 + 1)^2 + 353792*(tan(a)^2 + 1)^6)/(tan(a)^2 + 1) + 33600*tan(a)^4*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) + 20480*tan(a)^7*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 5040*tan(a)^2*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4) - 512*(tan(a)^2 + 1)^4*(2*tan(a) - tan(a)^2 + 1) - 960*tan(a)*(7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4) + 12349440*tan(a)^2*(tan(a)^2 + 1)^4 - 4423680*tan(a)^3*(tan(a)^2 + 1)^3 + 16727040*tan(a)^4*(tan(a)^2 + 1)^3 - 1382400*tan(a)^5*(tan(a)^2 + 1)^2 + 2845440*tan(a)^6*(tan(a)^2 + 1)^2 - 1680*(tan(a)^2 + 1)*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4) - 4608*tan(a)^8*(2*tan(a) - tan(a)^2 + 1) - 46080*tan(a)^5*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 16128*tan(a)^3*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) + 714240*(tan(a)^2 + 1)^5 - 5760*(tan(a)^2 + 1)^3*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 8064*tan(a)*(tan(a)^2 + 1)*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) + 28800*tan(a)^2*(tan(a)^2 + 1)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (11520*tan(a)^8*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (13440*tan(a)^6*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) + 20480*tan(a)^3*(tan(a)^2 + 1)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - (5120*tan(a)^9*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - (3360*tan(a)^4*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) + 8192*tan(a)^6*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) - 15360*tan(a)*(tan(a)^2 + 1)^2*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) + 46080*tan(a)^3*(tan(a)^2 + 1)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - (180*tan(a)^2*(256*tan(a)^8*(tan(a)^2 + 1) - 256*tan(a)^7*(tan(a)^2 + 1) - 15872*tan(a)*(tan(a)^2 + 1)^4 + 137216*tan(a)^2*(tan(a)^2 + 1)^4 - 49152*tan(a)^3*(tan(a)^2 + 1)^3 + 185856*tan(a)^4*(tan(a)^2 + 1)^3 - 15360*tan(a)^5*(tan(a)^2 + 1)^2 + 31616*tan(a)^6*(tan(a)^2 + 1)^2 + 7936*(tan(a)^2 + 1)^5))/(tan(a)^2 + 1) + (20*tan(a)*(353792*tan(a)*(tan(a)^2 + 1)^5 - 512*tan(a)^8*(tan(a)^2 + 1) + 512*tan(a)^9*(tan(a)^2 + 1) - 274432*tan(a)^2*(tan(a)^2 + 1)^4 + 1841152*tan(a)^3*(tan(a)^2 + 1)^4 - 371712*tan(a)^4*(tan(a)^2 + 1)^3 + 1304832*tan(a)^5*(tan(a)^2 + 1)^3 - 63232*tan(a)^6*(tan(a)^2 + 1)^2 + 128512*tan(a)^7*(tan(a)^2 + 1)^2 - 15872*(tan(a)^2 + 1)^5))/(tan(a)^2 + 1) + 3072*tan(a)^2*(tan(a)^2 + 1)^3*(2*tan(a) - tan(a)^2 + 1) - 7168*tan(a)^4*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) + (1024*tan(a)^10*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) + (15360*tan(a)^7*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (8064*tan(a)^5*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 51840*tan(a)^4*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + (960*tan(a)^3*(7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) - 26880*tan(a)^2*(tan(a)^2 + 1)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 5120*tan(a)*(tan(a)^2 + 1)^3*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 30720*tan(a)^5*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2);\r\n     };     \r\ns = S(x,n);\r\ns_correct = 0;\r\nfor  i = 1:n+1\r\n    s_correct = s_correct + Ts{i}(x) / 2^(i-1);\r\nend\r\ns_correct = round(s_correct,6);\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nfiletext = fileread('S.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-16T12:26:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2023-04-15T15:36:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-14T18:29:33.000Z","updated_at":"2023-04-16T12:26:21.000Z","published_at":"2023-04-15T14:27:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA trigonometric function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)=\\\\frac^{1+2\\\\tan(x)-\\\\tan^2(x)}_{1+\\\\tan^2(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                where:     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\tan^2(x) = \\\\tan(x)\\\\cdot\\\\tan(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIn this problem we are asked to evaluate the following summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=\\\\text{S}(x,n)=\\\\sum_{k=0}^n \\\\frac^{\\\\text{T}^{(k)}(x)}_{2^k}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                where:    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a real number; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}^{(k)}(x)=\\\\frac{\\\\mathrm{d}^k}{\\\\mathrm{d}x^k}\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th derivative of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}^{(0)}(x)=\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[  \u003e\u003e  syms x;\\n  \u003e\u003e  T = (1+2*tan(x)-tan(x)^2) / (1+tan(x)^2);\\n  \u003e\u003e  S = T/2^0 + diff(T)/2^1 + diff(T,2)/2^2;\\n  \u003e\u003e  s = vpa(subs(S,x,2))\\n        s = 0.10315887444431633673347091141408;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=0.103159\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eSymbolic toolbox is not available to Cody players. It is possible to do \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.unioviedo.es/compnum/labs/lab07_der_int/lab07_der_int.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumerical differentiation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in Matlab without symbolic toolbox.  Just make sure that the output would be accurate within 6 decimal places of the 'exact' value obtained using \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esyms\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, as shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55410,"title":"Easy Sequences 70: Inflection Points of Binomial Product Function","description":"Inflection points are points along the graph curve of a function, where the curvature of the curve changes from concave to convex, or vice versa. Consider the following the following binomial product function:\r\n                                \r\nwhere the coefficient  are given by the vector, . Write a function that outputs an array of the -coordinates all of the inflections of .\r\nFor example, if :\r\n                                \r\nThe plot of the function shows 2 inflection points:\r\n                                                \r\nTherefore, the function output in this case should be: . Please present the output rounded to 4 decimal places and sorted ascending.\r\n--------------\r\nNOTE: As an added challenge, some MATLAB built-in functions are disabled.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 740.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 370.25px; transform-origin: 407px 370.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Inflection_point\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInflection points \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325px 8px; transform-origin: 325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eare points along the graph curve of a function, where the curvature of the curve changes from concave to convex, or vice versa. Consider the following the following binomial product function:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" style=\"width: 420.5px; height: 45px;\" width=\"420.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 12.5px; height: 20px;\" width=\"12.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are given by the vector, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 212.5px; height: 20px;\" width=\"212.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.5px 8px; transform-origin: 112.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that outputs an array of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-coordinates all of the inflections of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 31.5px; height: 18.5px;\" width=\"31.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 141px; height: 18.5px;\" width=\"141\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" style=\"width: 359px; height: 45px;\" width=\"359\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153.5px 8px; transform-origin: 153.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe plot of the function shows 2 inflection points:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 358.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.25px; text-align: left; transform-origin: 384px 179.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96px 8px; transform-origin: 96px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 361px;height: 353px\" 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\" data-image-state=\"image-loaded\" width=\"361\" height=\"353\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169px 8px; transform-origin: 169px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, the function output in this case should be: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 117px; height: 18.5px;\" width=\"117\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePlease present the output rounded to 4 decimal places and sorted ascending.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242px 8px; transform-origin: 242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNOTE: As an added challenge, some MATLAB built-in functions are disabled.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ps = inflPoints(cs)\r\n    ps = cs;\r\nend","test_suite":"%%\r\ncs = [1 1 1];\r\nps_correct = -2;\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = [1 -1 1 -1];\r\nps_correct = [-1.5811 1.5811];\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = [1 2 3 4 5];\r\nps_correct = -7.6288;\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = repmat(2,1,5);\r\nps_correct = -6;\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = repmat([1 -2],1,6);\r\nps_correct = [0.5394 10.7378];\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = repmat([1 -1 1],1,5);\r\nps_correct = [1.1646 8.4726 10.8803];\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs1 = ones(1,10); cs2 = [1 -2 -3 4 5 -6 7];\r\ncs3 = repmat([1 -4],1,3); cs4 = repmat([3 -2],1,6);\r\ncs5 = [2 4 6 -8 -9 -10]; cs6 = (1:6).*3.-2;\r\nps = sort([inflPoints(cs1),inflPoints(cs2),inflPoints(cs3),inflPoints(cs4),inflPoints(cs5),inflPoints(cs6)]);\r\nps_correct = [-30.1765 -18.6599 -17.6178 -14.2587 -5.9861 -4.6735 -1.1563 1.9772 2.8718 10.2251 19.8482];\r\nassert(isequal(ps,ps_correct))\r\n%%\r\nfiletext = fileread('inflPoints.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java') ...\r\n|| contains(filetext, 'sum') || contains(filetext, 'prod') || contains(filetext, 'if') || contains(filetext, 'for') || contains(filetext, 'while') ...\r\n|| contains(filetext, 'switch') || contains(filetext, 'try') || contains(filetext, 'assignin') || contains(filetext, 'arrayfun') || contains(filetext, 'conv') ...\r\n|| contains(filetext, 'cellfun') || contains(filetext, 'bsxfun')  || contains(filetext, 'solve') || contains(filetext, 'zero');\r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-09-04T10:58:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-02T17:36:31.000Z","updated_at":"2022-09-04T10:58:02.000Z","published_at":"2022-09-02T20:44:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Inflection_point\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInflection points \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003eare points along the graph curve of a function, where the curvature of the curve changes from concave to convex, or vice versa. Consider the following the following binomial product function:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x)=\\\\sum_{i=1}^{n}(x+c_1i)(x+c_2i)(x+c_3i)...(x+c_{n-2}i)(x+c_{n-1}i)(x+c_ni)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are given by the vector, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ecs = [c_1,\\\\ c_2,\\\\ c_3,\\\\ ...\\\\ c_{n-2},\\\\ c_{n-1},\\\\ c_n]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that outputs an array of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-coordinates all of the inflections of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ecs=[1,\\\\ -1,\\\\ 1,\\\\ -1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x)=\\\\sum_{i=1}^{4}(x+i)(x-i)(x+i)(x-i) = 4x^4-60x^2+354.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe plot of the function shows 2 inflection points:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"353\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"361\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, the function output in this case should be: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[-1.5811,\\\\ 1.5811]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePlease present the output rounded to 4 decimal places and sorted ascending.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e--------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: As an added challenge, some MATLAB built-in 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52973,"title":"Easy Sequences 45: Second Derivative of Inverse Polynomial Function","description":"The inverse of a function, is the function , that reverses . That means that if , then . For example, the function to convert celsius temperature to fahrenheit is: , the inverse function (convert from fahrenheit to celsius) is: . So that,  and .\r\nGiven a polynomial function  (presented as vector of numbers), and a value , if , write a program that evaluates , where . \r\nFor example, if , and , then  and . Therefore .\r\nNOTE: It is possible for  to return some complex numbers. We are interested only with real values, so in cases where there are no real , please output an empty vector. Also please round-off your output to 4 decimal places, and sorted in ascending order.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 299.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 149.75px; transform-origin: 407px 149.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 77px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 38.5px; text-align: left; transform-origin: 384px 38.5px; white-space: pre-wrap; margin-left: 4px; 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height: 18.5px;\" width=\"32.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 19.5px;\" width=\"44\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.5px 8px; transform-origin: 47.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that reverses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63px 8px; transform-origin: 63px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. That means that if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 58.5px; height: 18.5px;\" width=\"58.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 70.5px; height: 19.5px;\" width=\"70.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.8667px 8px; transform-origin: 15.8667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the function to convert celsius temperature to fahrenheit is: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 97.5px; height: 28px;\" width=\"97.5\" height=\"28\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112px 8px; transform-origin: 112px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the inverse function (convert from fahrenheit to celsius) is: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 121px; height: 28px;\" width=\"121\" height=\"28\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.5px 8px; transform-origin: 30.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. So that, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 88px; height: 18.5px;\" width=\"88\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 100px; height: 19.5px;\" width=\"100\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 58px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 29px; text-align: left; transform-origin: 384px 29px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.5px 8px; transform-origin: 99.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a polynomial function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167px 8px; transform-origin: 167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e (presented as vector of numbers), and a value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.5px 8px; transform-origin: 10.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 91.5px; height: 19.5px;\" width=\"91.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.5px 8px; transform-origin: 29.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a program that evaluates \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 74px; height: 37px;\" width=\"74\" height=\"37\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 74.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 37.25px; text-align: left; transform-origin: 384px 37.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 189.5px; height: 19.5px;\" width=\"189.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" style=\"width: 186.5px; height: 37.5px;\" width=\"186.5\" height=\"37.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.5px 8px; transform-origin: 37.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 208.5px; height: 18.5px;\" width=\"208.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51px 8px; transform-origin: 51px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt is possible for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 293.5px 8px; transform-origin: 293.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to return some complex numbers. We are interested only with real values, so in cases where there are no real \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311px 8px; transform-origin: 311px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, please output an empty vector. Also please round-off your output to 4 decimal places, and sorted in ascending order.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = R(P,n)\r\n  y = x;\r\nend","test_suite":"%%\r\nP = [3 -7 2]; n = 5;\r\nr_correct = [-0.0077 0.0077];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 2 0]; n = 1;\r\nr_correct = [-0.0884 0.0884];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 2 3 4]; n = 5;\r\nr_correct = [-0.0696];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 -10 35 -50 25]; n = 1;\r\nr_correct = [-0.2500 -0.1019 0.1019 0.2500];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = 10:-2:2; n = -3;\r\nr_correct = [];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 -5 -10 -10 -5 1]; n = 0;\r\nr_correct = [-0.0458 0.0000 0.0400];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = ones(1,25); n = 1;\r\nr_correct = [-2.0000 0.1667];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = repmat([7 -2 3],1,1000); n = 4;\r\nr_correct = [-0.0785 0.0000 0.0001 0.0445];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 -3 -3 1]; ns = -10:0.1:10;\r\ns = arrayfun(@(n) sum(abs(R(P,n))),ns);\r\nss = round([sum(s) median(s) mean(s) std(s)],4);\r\nss_correct = [60.5806 0.0202 0.3014 1.8229];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('R.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2021-11-01T04:59:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-24T05:55:27.000Z","updated_at":"2026-03-24T13:06:02.000Z","published_at":"2021-10-30T16:02:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Inverse_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003einverse of a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef^{-1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that reverses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That means that if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(a)=b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef^{-1}(b)=a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the function to convert celsius temperature to fahrenheit is: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(x) = \\\\frac_{9}_{5}x+32\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the inverse function (convert from fahrenheit to celsius) is: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT^{-1}(x) = \\\\frac_{5}_{9}(x-32)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. So that, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(100)=212\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT^{-1}(212)=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a polynomial function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e (presented as vector of numbers), and a value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ(x)=P^{-1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a program that evaluates \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)=\\\\frac{\\\\mathrm{d^2Q} }{\\\\mathrm{d} x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = [3\\\\ -7\\\\ 2]=3x^2-7x+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ(x)=P^{-1}(x) = \\\\frac{7}{6} \\\\pm \\\\frac{\\\\sqrt{12 x + 25}}{6}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)=\\\\frac{\\\\mathrm{d^2Q} }{\\\\mathrm{d} x^2}=\\\\pm\\\\frac{6}{\\\\left(12x+25\\\\right)^{3/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(n) = R(5) \\\\approx [-0.0077\\\\ 0.0077]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eIt is possible for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to return some complex numbers. We are interested only with real values, so in cases where there are no real \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, please output an empty vector. Also please round-off your output to 4 decimal places, and sorted in ascending order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54750,"title":"Find the length of stream affected by a spill","description":"When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration  is often computed as a function of time  and distance  from the spill using the advection-dispersion equation:\r\n\r\nwhere  is the mean velocity of the river and  is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass  mixed over the cross section (with area ) at , the concentration can be shown—using some of the math needed for Cody Problem 51625—to be\r\n\r\nWrite a function to compute the length of stream affected by the spill. In other words, find the position  (say) beyond which the concentration never exceeds a threshold . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 282.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 141.35px; transform-origin: 407px 141.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.317px 8px; transform-origin: 378.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.675px 8px; transform-origin: 123.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is often computed as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.833px 8px; transform-origin: 168.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the spill using the advection-dispersion equation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dC/dt + U dC/dx = K d^2C/dx^2\" style=\"width: 126.5px; height: 36.5px;\" width=\"126.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.158px 8px; transform-origin: 202.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.242px 8px; transform-origin: 125.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e mixed over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 8px; transform-origin: 12.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration can be shown—using some of the math needed for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51625\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51625\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5583px 8px; transform-origin: 22.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—to be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.05px; text-align: left; transform-origin: 384px 20.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\" style=\"width: 204.5px; height: 40px;\" width=\"204.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.617px 8px; transform-origin: 313.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = L_a\" style=\"width: 42.5px; height: 20px;\" width=\"42.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3417px 8px; transform-origin: 44.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) beyond which the concentration never exceeds a threshold \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = C_t\" style=\"width: 46px; height: 20px;\" width=\"46\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function La = affectedReach(U,K,M,A,Ct)\r\n% La = length of affected reach of stream [L]\r\n% U  = mean velocity [L/T]\r\n% K  = dispersion coefficient [L^2/T]\r\n% M  = mass of contaminant [M]\r\n% A  = cross-sectional area (L^2)\r\n% Ct = threshold concentration (M/L^3)\r\n\r\n  La = M/(Ct*A);\r\nend","test_suite":"%%\r\nM = 100;                    %  Mass (kg)\r\nA = 30;                     %  Cross-sectional area (m2)\r\nU = 0.3;                    %  Mean velocity (m/s)\r\nK = 2;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 50;                     %  Mass (kg)\r\nA = 15;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 8.4;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.001;                 %  Target concentration (kg/m3)\r\nLa_correct = 26332.1;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 0.003;                 %  Target concentration (kg/m3)\r\nLa_correct = 91.59;         %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 3e-4;                  %  Target concentration (kg/m3)\r\nLa_correct = 7256.28;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 70;                     %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.15;                   %  Mean velocity (m/s)\r\nK = 1;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 280;                    %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.54;                   %  Mean velocity (m/s)\r\nK = 3.7;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.007;                 %  Target concentration (kg/m3)\r\nLa_correct = 42140.42;      %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%% Approximately plug flow\r\nM = 5*rand;                 %  Mass (kg)\r\nA = 40;                     %  Cross-sectional area (m2)\r\nU = 0.3*(1+rand);           %  Mean velocity (m/s)\r\nK = rand*1e-3;              %  Dispersion coefficient (m2/s)\r\nCt = 0.02*rand;             %  Target concentration (kg/m3)\r\nLa_approx = (U/(4*pi*K))*(M/(Ct*A))^2;\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_approx)/La_approx\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('affectedReach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'if'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-14T05:04:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-06-14T05:04:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-14T04:57:20.000Z","updated_at":"2022-06-14T05:04:44.000Z","published_at":"2022-06-14T04:59:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is often computed as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the spill using the advection-dispersion equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + U dC/dx = K d^2C/dx^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t} + U \\\\frac{\\\\partial C}{\\\\partial x} = K \\\\frac{\\\\partial^2 C}{\\\\partial x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e mixed over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the concentration can be shown—using some of the math needed for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51625\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51625\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—to be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L_a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L_a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) beyond which the concentration never exceeds a threshold \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = C_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = C_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52562,"title":"Easy Sequences 6: Coefficient sums of derivatives","description":"Consider the polynomial function  and its first-order derivative . The sums of the coefficients of P and P', are  and , respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows:  etc.  The total sum of this sequence converge to .\r\nFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, . Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 98px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the polynomial function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"163\" height=\"20\" style=\"width: 163px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and its first-order derivative \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"35\" style=\"width: 129.5px; height: 35px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. The sums of the coefficients of P and P', are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"120\" height=\"18\" style=\"width: 120px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANgAAAAkCAYAAADrcPSPAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAA2KADAAQAAAABAAAAJAAAAABhLo42AAAH2ElEQVR4Ae2ae8zXUxzHu0gPKZVoaV1VzIiW3Ld02TSXdFEkZc1iY1pDxuSuy4bNH5qhzB9szLoTi0h/5ClKEuZaDQm1LpRu4vXO97TzfPvev79vz/fpOZ/t/XzPOZ/POedzOfff06CBI+cB5wHnAecB5wHnAecB5wHnAecB5wHnAecB5wHnAecB5wHnAeeBKA80jGL6eJ3JTwBTwRaQhC5AKKiP5pQ/7GFZkoZqWaYR/d8EqsDMBLo0QaYf6Al6gPXgY7AS7AZlppYo1z2FgmuR3ZtCvrZE88akHYpfD7qBf8D7YCnIHc8ONPIC2Af+BeogCV2JkOTDsAmejC4zaWLdCL4GsuNVEEfnIbAGBNm9lfKL4hqoZf6zIboH2aOyjrWsb5Lu88bkLjrRInIQLAXLgWzfA8aCTNSeWs8BNWw7N+kEW+KrZ7eh9COgrKRddzj4Ath6x00wrfxa0ew6/vSf8PuDMtIJKLUN+HUOy39bRiN8OuWNya20p4klDLDavpq0/KLd7GarPHFyNpJPgDFgPzBOTjLBenvyH/J9PAA6ajYDZaWrUGwekOMWAGN71ATTpFwG5PBpQEeKxuAML29OAGrrU1BGGodS0u8TMBEo9vKBH1okJDcdlJnyxmQgximeslWnOD/NokC8A6CXn5kmvw5hNSQkmWCvIyfFtHoUTYPpQAN7YUEd6dxtbI+aYJd4cpND9BhvtSPftAqRq83iFXS+GBwfocSp8DSg5JM+EXJlYOWNyVuenbI1aCz3sPiabJmpmppmkMVNsK7IKgBapVuAoul2OpBuSR9e0uozyGtffURNsCnwdVdrBIJIq+l3wPhRC0OZqApllgDtvFF0G0zZsDFKqCS8PDGRH8xCsinCns3w5A9dDVr75cIGg18uTf5uhHU00jFR53m9Mj0NeoJjmVpi3KNAZ/UgUhA+txhhcpbIUU3qwj4A/BrT6wiPPydGrgzsPDEZjQEaxyKdkMLI8HR/HeUXqvQEO4UOdI43pPbPBfcADa75oC04FulOjHojxjANYkM/mkQd+up42M/TV3f0slOemNgbgk4mYfSlxTjLSh9KVnqCnUSrH4ANQCu2n3Qs0gX6dD+jnuQ7e3bq9e2rOmjzEHTWqq5j0fI6qH+Qyp29Qn9M9IpuaLtJBHx3WGUdrfSh5HH+gpx5ncuv9dpoxvdscAcYC8xk7kBal0ddkHXZry90Goaa38Cer6NGm+PhXPQ/mMEGHSv7ZqjnrzKSAt0X81JUTOxNIGqC2bwjJlhSBasR1I4kxD1yBLXZi0KteKYNfXXGrQSV5ZEjzpZJCMhuHZWbxAmXkN8GnfYD2aC7WhZ6j0r2GMiaHpSl84A6UTGxfw/Uzh1Gw2EYO37xC1V6B/O3b/KfkZBT9LLY3SvUXe01L32sf/Qi9SDQHUx2a6DWNdIg03jZCj7KqPx06r2Zsa5dbZWdyZiOi8nftNvSa7thRB/2HDKPIofFbebhwoISO2l3GFgDpEgnkIR0rFoUIVjl8VrzVfDDSDuoOb6GyRRRruDMAC3ADWA1SEsLqXBp2ko++dHk3/WVpcma4+ECKun5OgvpWFeJo12Wvu06SWLyGxU0CUUn//8J/KvXQ0OqU4OO5gRTx+vAN0B3M51/k5B01OSJIzktSk4DvDboMTodCu4DWVdv6R5lG+xYynMs1etwf6+H2bE9lV8gSUzsyWJ2siDLbN4RP3Ec7QkmBbWCa4JtVyYB6Xg5HphHEn8V7UrXgL1ggp9p5Y8w3uIVldTjzkNAR6OncnTyJHW75Kivqmtz1B9CXY2VnUD3qLpMSWPys2WkPYms4kNJmxf1g7S/Xo18NTlzketWg5M+85LXltqsBJX1keM6jNNdq66+GNqx0dFS8c97Z55DGzrG50XWR5Y0MbEfL+aicxjJJjM3xoQJxZVXcoKt9BR6IK7ThPwyTjANAD1oaECG7byt4GlnKjvpeKiFQoNoWE5ltfuZwZjnOyiDHmljorvVX56+W/jqCuInlWmxkC27gH4HrkHa9pNQUONJ6vllLqegD1DAZvmZJc2ntf1i7JgPFoNbQNDvRboPvQJ2g7KTVn2NE+ma55FEdk4HWe+hqm9olUkk/GaJiV4R3wYjgRaZnkA/sdh0PhlzN55HWhOyBiWdYG2tWlVW2k42JSOFdL9aASaB74EhKTnDy4j3u2GU/JvEdmOCgrAINAMK0EzgJwXkMqBv1qOOv80i8yO8xt/hm3dB0AuicDQpT0wmo+hAoFhNAbrr2zTVy+zgO81mJE03RnAisLfzZ8hrBfaTDLHlNMB0DDwTKEj6VxTx7wWVpCKPiF1RVKuWsesP0rIniHpQuBkY2bivFp+0u2NQv0WWaWDtA7JlVJEdFdR2JWLSF930gCYfaGNo6uF+r2wP3ytAatJ2bs6g/sGiGbsuoMWXKdORyC+vsjmgN6g0FTHB2qPkTyDMlvXw1K9Nae8XClDZaRwKKpYaRM3LrmyAfpWKyVDa3gjki20elFbZYBBKRaygXejtHNAO7AQbwA9Aq38RNJ5GXwS6bLYpooN63GYnbO8IdoHV9dgPMl2ntgtBN2UgjelqcECZMCpigoX1VVT5iTSsy6YM1QulI+cB5wHnAecB5wHnAecB5wHnAecB5wHnAecB5wHnAecB5wHnAecB5wHnAecB5wHnAeeB/wA2WWDXBrcNEgAAAABJRU5ErkJggg==\" width=\"108\" height=\"18\" style=\"width: 108px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALQAAAAkCAYAAAAgqxBxAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAtKADAAQAAAABAAAAJAAAAACH07FpAAAG+ElEQVR4Ae2ZaahWRRjHXdLUyrTFMEOvuVTiErSY2XrNkjBLKKPMun4w+6QRFC2SSWX2oSRSCipQyRYTbwUFaQgqtGcrRiUp2mKLCq65tPz+OoPDcM5533vf98w973Ue+L8z8zzPzDzznzlz5szbpk2UyEBkIDIQGYgMRAYiA5GByEBkIDIQGYgMRAYiA62BgfYFGMQpxDAPDAGrWyCefvQ5FkwC48DJYDfYDkpJWxzGANWdCPoC1dsKiiLl8tuBgK8C40EDGAyOAX+AAyBKmQy8id9/4IMy/avlpgmcCfYD9e9jAbqsB74H9i9NPU36UrDNlDWWbqAIUg6/wwjUjsXnQQ/n8CIMpBZimEKQlsDQC/oFp28bg5824tMxgcju6L4y9d8n1cMhORasAWrnE3AiaEkph98BBLgH+GN3yzux17fkQGqhbxG5C1jiQi7o0abfb0lHgU5Ai+9q8DWwMSnVccSXVShk00Lo5xkHUt4LZF/m2UIWy+FXRyYd8/4BT4CeQG8ljUll9+31GeUoKQzobPYx2AD+Bpr8kAv6Pfr7GZwGfOmMYj1QTMJc4Mr5FKxtsWtw8q8YHy2UOkcfKlsuvyMISGOZkRLYFGOXj8aiN1OUBAYeRSeCLgU6f4qwUAv6ePraB24BaTIJg120az2n+Y5tqmezxbscnzlWGTAtl9/Hiek70C4lNu3gPwLLhT6ao3gMjKR8EOiVJgm9oIfS5wqgV2uaDMZgJ9F91XZAv82xnZ3SwCDHR+MLKU3hVw/nzSWCW4rdcjG2hO9RZz6BEf8EtOtpcUhCL+jDvWb/9sdsJ3GJ43qmo9cbRjtYkkgvu21DV4EhJA9+XyZwOw49qIWWtFdNXkHPo+Ge4DZwIK9OqtBundOGrr2s9LIZ0h1AE50k0utmwEpvm8k5zYPfOhPzD6Trco6/ppq/iWg10dO8qIu4Qz9jYt1C2smJV69nu1ttcPRJ2Y2O7/VJDlXW5cGv7tq18WjMd1c53ppu7gyi19lzOfBf00Vb0F2I0cY0gbwr0ynYBa0/IrLkG4zWV7cFeUpe/N5L0BqD7tztETHPcVTcdogjhxbwQiBiGkxKUliZSWSngiUGbqB7nYL/YDqmQ1ldnVnJ+gC1Ps1N8+JXR8OHgK5VJ4MiHxEJ77C4pFvdUDIrQakJs/5Jqf6cuNIY7iGtB9rtfjW6oia6Y1a8n4IG4MvvjkJ/xGSJ7rOtuPWsrlppHvxq7ueDrkDHrLWgJiRpQeuLvNKvchEh0bXWbPA92AGuAb7oy1zSDVj7HvJrpAwoem2/BTaBccDdjSkeEndhKt4sce2/ZTlWYMuL31nENB7cB96oIL7gVZN24dOJotL7xr9oYxm4ATSCpoqu9vo1tVIF/noAV4Ee4BKwASSJFv1mY9ARShvCv6bsJjrKHQSW3z7k9aBUW/Lg93aCXAjmgAeqHXCtt6eve93HZkELw8L66YoolOhooMWsh3BQGZ26H3vDUvyHordjWp/iUw11tflVezorP1eN4I7WNuyNQqi/vl2e9eX+DtBx6ALX4OUbKF9odA+T2sU6zej8ZLrjM8s3Bi6Xy+8o4tIH4GKgN0ySdEf5WJIh6o4wUIpwLTodgW4Exx2pVnFOk/Y60Fn5CpAml2HQRJ9lHM4htQu60ej8RGdx6zPAM/alPBkM8/R5FUvxq34vArvA2yDpuwr1oWs7jetVFYw0Z27aU3c06G8b8VId664FHT29iqXqJlQJrypFuEi2i+Nz8jrvViptaeBFoHZ187IgAYvQfQF0DFoNXHmWgurKNtw1kL/Y6GV/ybOdR1lnbtl0xr4D5C2l+NXxaBtQTHrAFyRAc7AVyKceWGnO3OiNqHbEw7m2IZOOIBUvsidtFll1TRMtn2QR3o7w9gMN0GJCFUJ+2mnPtpuVTvL61E7xrmljHekAYx9IqhsdtSXy/d1uhrHZvlQ3b8niV/FuATaeUul6fLUZSJozN3rD2gdafc1WQ448Sd7GoM2ik2MrVddxbdnsJrrXIFamhKFrIztIpY+k+JWrHomj216p/Hb8Oyc0ruvG14CIVxsbTaqyXstdgC96te8Etk/5amHkKVn8rqBjG0s56f1eoM2Zmw9Nn9qJL/faG0PZLnjF5ktWXd+30GXtJBOBSL+1YJH2Jp7rwFQwDqicJbqfHgQ+AiFvc7JiqsTW1LnRg66F2yulU32j1IOkB71U3ZQmi6l+nrD+BF2LGV6TouqD9z7wYJNqFde5Nc1N7izrSZ0LdgPtgLUuQxjAZrAcJB1laml8rW1ugnB/J71sBP4XcZDOc+jkF9p8CujDstaltc1NkPnQEeOkID2F6aQuTDdBemltcxOEtNhJZCAyEBmIDEQGIgORgchAZKBIDPwPOJEp8UY8O6EAAAAASUVORK5CYII=\" width=\"90\" height=\"18\" style=\"width: 90px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e etc.  The total sum of this sequence converge to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAJKADAAQAAAABAAAAJAAAAAAqDuP8AAACUElEQVRYCe2WT0tWQRTGrwVZQRGYiwhpVQgZSbRp4cLy3bmxPkCt8iO4zhZt/ABGBEbbWrboCxS4UIsUiWphtIhIzEQLsvo915mXc+fOa9BBV/fAc+f8mfOcw9y5c6coGmlWoFmBvV2Brn/QHyU+Cs6BM+ArWAJPwCbYTTy5Wd5xvJ/BL/AcPAZvwB8gfwt0Ek9ulvMmXhVeBQNmhlb0DlDsOxgEqXhyU67SPshzHajoROmpPg5gLgLF71dDhSe3pBJ5KhdwHAvOD2kQ+zd4FfxDSdyTW1LlGjptilw0ulVPBUPNWfHkWp6Krib0OoRvwBbBLPT1/ASKPwJWPLmWp6bHr0lF34I+M2MKXX5t+LPGH1VPbuSojVfw/AAqHIvfRn8Y7HeM50FOPLk5vrbvBlp8NbExjdPgcHtWXvHk5hmDd5jRNiNdh+JIiO82eHKzvNq82rRqQr8J29g2tl5hJ/HkZjmP430B1MQMOALuATUSG5N+HaTiyU252vYDNBXWj7S77d15VV9CTPFPSVxTPbnKr8klPDrwVHCyFi0KxTdCXHPGzBxPbkmTO6kvE+kKRWZNsajOoej6EcWeRZ7cki/X0IlYiVGHX06eGaf2UhRPbsmRa+hlZGfsN7pVV4yxbHRPrqGpqocw14H2x2ugK0Uqd3EovgZ6TNCTa2jq6jVcW0BFn4KTIMotlHiC60ROxZObclXsq1gLQE1pn7wH2lOy50ELdJL/zo1fUydi+XXp0pfUCz4C/f11cUvvQrhq4smtkTWOZgWaFWhWYD9W4C/P++GDxZTKPgAAAABJRU5ErkJggg==\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"98.5\" height=\"19\" style=\"width: 98.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function totSum = tot_dCoefSum(coef)\r\n  y = x;\r\nend","test_suite":"%%\r\ncs = [5 6 -7 -8];\r\nts = '88';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [3 15 -2 1];\r\nts = '120';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [-7 22 43 6 -75 3 1 0 -80 10 5];\r\nts = '-42698751';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = 1:25;\r\nts = '1836856501837772435875025';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = repmat([2,-1],1,15);\r\nts = '47298214022376392514505945712317';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [ones(1,20) zeros(1,10)];\r\nts = '24893912605687593731774059567276';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = repmat([-2,-25,1],1,10);\r\nts = '-68761759219969440143678420163128';\r\nassert(isequal(tot_dCoefSum(cs),ts))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2021-08-17T17:53:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-16T19:00:56.000Z","updated_at":"2025-11-30T19:39:34.000Z","published_at":"2021-08-17T12:43:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the polynomial function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\\\\left(x\\\\right)=5x^3+6x^2-7x-8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and its first-order derivative \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dP}{dx}=15x^2+12x-7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The sums of the coefficients of P and P', are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5 + 6 - 7 - 8 = -4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e15+12-7= 20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-4,\\\\ 20,\\\\ 42, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e etc.  The total sum of this sequence converge to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e88\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 6\\\\ -7\\\\ -8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57874,"title":"Easy Sequences 107: Minimized Circumcircle-Incircle Areas Ratio of Partial Pythagorean Triangles","description":"We define a Partial Pythagorean Triangle (PPT) as a right triangle wherein the hypotenuse and at least one leg are integers. Thus, the triples  and  represent a PPT, while ,  and  do not.\r\n\r\nGiven the limit , find the area of the PPT with perimeter  , such that the ratio of the areas of the triangle's circumcircle to its incircle, ,  is as small as possible.\r\n                                                              \r\nPlease present the answer rounded-off to the nearest integer.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 427px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 213.5px; transform-origin: 407px 213.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 50px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 25px; text-align: left; transform-origin: 384px 25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe define a Partial Pythagorean Triangle (PPT) as a right triangle wherein the hypotenuse and at least one leg are integers. Thus, the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62\" height=\"19\" style=\"width: 62px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"79.5\" height=\"21\" style=\"width: 79.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e represent a PPT, while \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"79.5\" height=\"21\" style=\"width: 79.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67\" height=\"29\" style=\"width: 67px; height: 29px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62\" height=\"19\" style=\"width: 62px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e do not.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 61px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 30.5px; text-align: left; transform-origin: 384px 30.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003earea of the PPT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with perimeter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"26.5\" height=\"18\" style=\"width: 26.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e , such that the ratio of the areas of the triangle's circumcircle to its incircle,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36\" height=\"40\" style=\"width: 36px; height: 40px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e is as small as possible.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 238px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the answer rounded-off to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = areaPPT(P)\r\n  y = x;\r\nend","test_suite":"%%\r\nP = 20;\r\nA_correct = 12;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 50;\r\nA_correct = 72;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 100;\r\nA_correct = 420;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 500;\r\nA_correct = 2450;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 1000;\r\nA_correct = 28561;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 5000;\r\nA_correct = 485112;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 10000;\r\nA_correct = 2827442;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 50000;\r\nA_correct = 16479540;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 123456;\r\nA_correct = 642216964;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 1234567;\r\nA_correct = 36092590380;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 12345678;\r\nA_correct = 36092590380;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 123456789;\r\nA_correct = 35239028445009;\r\nassert(abs(areaPPT(P)-A_correct)\u003c=0.01)\r\n%%\r\nP = 987654321;\r\nA_correct = '36028897335524829';\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 12345678910;\r\nA_correct = '2319322204054392180';\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 1e7:2e6:1e8;\r\nA = arrayfun(@areaPPT,P);\r\nS = round([mean(A) median(A) mode(A) std(A)]);\r\nS_correct = [27586216302698 35239028445009 35239028445009 14680639085634];\r\nassert(isequal(S,S_correct))\r\n%%\r\nfiletext = fileread('areaPPT.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-10T18:10:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-02T12:05:10.000Z","updated_at":"2026-03-13T20:20:14.000Z","published_at":"2023-04-10T18:09:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe define a Partial Pythagorean Triangle (PPT) as a right triangle wherein the hypotenuse and at least one leg are integers. Thus, the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{3,\\\\ 4,\\\\ 5\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1,\\\\ \\\\sqrt{3}, \\\\ 2\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e represent a PPT, while \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1,\\\\ 1,\\\\ \\\\sqrt{2} \\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{\\\\frac^{3}_5,\\\\ \\\\frac^{4}_5,\\\\ 1\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{{4.\\\\ 4,\\\\ 4\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e do not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003earea of the PPT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with perimeter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e , such that the ratio of the areas of the triangle's circumcircle to its incircle,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left(\\\\frac^{A_c}_{A_I}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e is as small as possible.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                              \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"232\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"256\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the answer rounded-off to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpeg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpeg\",\"contentType\":\"image/jpeg\",\"content\":\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAM2OQAAkpIAAgAAAAM2OQAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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Magnitude Calculator","description":"'a' is a vector that starts at the origin and ends at (x, y). Find ||a||.\r\n\r\nHint: It is as simple as \"ABC\".","description_html":"\u003cp\u003e'a' is a vector that starts at the origin and ends at (x, y). Find \u003ctt\u003e|a|\u003c/tt\u003e.\u003c/p\u003e\u003cp\u003eHint: It is as simple as \"ABC\".\u003c/p\u003e","function_template":"function m = vector_magnitude(x, y)\r\n  m = x;\r\nend","test_suite":"%%\r\nx = 5;\r\ny = 12;\r\nmm = 13;\r\nassert(isequal(vector_magnitude(x, y),mm))\r\n\r\n%%\r\nx = 3;\r\ny = 4;\r\nmm = 5;\r\nassert(isequal(vector_magnitude(x, y),mm))\r\n\r\n%%\r\nx = 12;\r\ny = 35;\r\nmm = 37;\r\nassert(isequal(vector_magnitude(x, y),mm))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":26349,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":167,"test_suite_updated_at":"2014-06-05T15:55:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2014-05-07T19:54:35.000Z","updated_at":"2026-02-18T09:28:19.000Z","published_at":"2014-05-07T19:54:35.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e'a' is a vector that starts at the origin and ends at (x, y). Find\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e|a\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e|.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHint: It is as simple as \\\"ABC\\\".\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":685,"title":"Image Processing 2.1.1 Planck Integral","description":"Integrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\r\n\r\nPlanck  Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\r\n\r\nc1'=1.88365e23; % sec^-1 cm^-2 micron^3\r\n\r\nc2=1.43879e4;  % micron K\r\n\r\nMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\r\n\r\nRadiance  :    L = Me/pi in units of ph sec^-1 m^-2\r\n\r\nInput:  (3.0 5.0 250)  : From 3um to 5um at 250K\r\n\r\nOutput:  4.9612 E+018  : units ph/sec/m^2/ster\r\n\r\nPerformance Rqmts: \r\n\r\nAccuracy: \u003c0.001% error\r\n\r\nTime: \u003c100 msec (using cputime function)\r\n\r\n\r\nCorollary problem will include spectral transmission and emissivity.\r\n\r\n\r\nIR Calibration Reference:\r\n\r\n\u003chttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003e","description_html":"\u003cp\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/p\u003e\u003cp\u003ePlanck  Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/p\u003e\u003cp\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/p\u003e\u003cp\u003ec2=1.43879e4;  % micron K\u003c/p\u003e\u003cp\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/p\u003e\u003cp\u003eRadiance  :    L = Me/pi in units of ph sec^-1 m^-2\u003c/p\u003e\u003cp\u003eInput:  (3.0 5.0 250)  : From 3um to 5um at 250K\u003c/p\u003e\u003cp\u003eOutput:  4.9612 E+018  : units ph/sec/m^2/ster\u003c/p\u003e\u003cp\u003ePerformance Rqmts:\u003c/p\u003e\u003cp\u003eAccuracy: \u0026lt;0.001% error\u003c/p\u003e\u003cp\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/p\u003e\u003cp\u003eCorollary problem will include spectral transmission and emissivity.\u003c/p\u003e\u003cp\u003eIR Calibration Reference:\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\"\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/a\u003e\u003c/p\u003e","function_template":"function Radiance = Calc_Radiance(Lo,Hi,T)\r\n% Lo wavelength um\r\n% Hi wavelength um\r\n% T  Blackbody Temperature (K)\r\n\r\n  Radiance = T;\r\nend","test_suite":"%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=250.0;\r\n% Radiance = 4.96124998 e18 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.96124998e18; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=300.0;\r\n% Radiance = 4.1826971 e19 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.1826971e19; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=8.0;\r\nhi=12.0;\r\nT=280.0;\r\n% Radiance = 1.37122128 e21 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 1.37122128e21; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\n\r\n% Add random to block answer writers\r\nlo=3.0+rand\r\nhi=5.0+rand\r\nT=250.0;\r\n% Radiance = To be calculated ph/m2/sec/ster\r\n\r\nc1p=1.88365e23; % sec^-1cm^-2micron^3\r\nc2=1.43879e4;  % micron K\r\nsteps=1000;\r\n\r\nx=lo:(hi-lo)/steps:hi;\r\n\r\n% Planck Vectorized for Trapz\r\ny=1e8./(x.^4.*(exp(c2./(x.*T))-1));\r\n% Leading 1e8 is for numerical processing accuracy\r\n\r\nz=trapz(x,y);\r\nrad_correct=z*1e4*c1p/pi()/1e8 % 1e4 normalizes from cm-2 to m-2\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-14T04:31:21.000Z","updated_at":"2025-12-10T03:26:46.000Z","published_at":"2012-05-14T05:39:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec2=1.43879e4; % micron K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRadiance : L = Me/pi in units of ph sec^-1 m^-2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: (3.0 5.0 250) : From 3um to 5um at 250K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: 4.9612 E+018 : units ph/sec/m^2/ster\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePerformance Rqmts:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAccuracy: \u0026lt;0.001% error\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCorollary problem will include spectral transmission and emissivity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIR Calibration Reference:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":58259,"title":"Easy Sequences 115: Integral involving square root, floor, and round functions","description":"Given a postive real number , we are asked to evaluate the following integral:\r\n                            \r\n                            where:     the symbol \"\" is the floor function,\r\n                                            and \"\" is the round (to the nearest integer) function.\r\nWe may rewrite the above function in Matlab as:\r\n\u003e\u003e  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\r\nTherefore, for , we have:\r\n\u003e\u003e  s = S(10*pi)\r\ns =\r\n        12\r\nBe careful though, in using the Matlab integral function, as it is only an approximation. For example if :\r\n\u003e\u003e  s = S(100000)\r\n\r\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\r\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\r\nrequested accuracy. \r\n\u003e In integralCalc/iterateScalarValued (line 372)\r\nIn integralCalc/vadapt (line 132)\r\nIn integralCalc (line 75)\r\nIn integral (line 87)\r\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \r\n\r\ns =\r\n       49841\r\nThe correct answer is . The integral function is off by only 2 units here, but the discrepancy could be even greater for other values of . integral function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 673px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 445.71875px 336.5px; transform-origin: 445.71875px 336.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a postive real number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, we are asked to evaluate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 48px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 24px; text-align: left; transform-origin: 384px 24px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-18px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"247.5\" height=\"48\" style=\"width: 247.5px; height: 48px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                            where:     the symbol \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/floor.html#\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003efloor\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function,\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                            and \"\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"23.5\" height=\"19\" style=\"width: 23.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\" is the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/round.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eround \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e(to the nearest integer) function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe may rewrite the above function in Matlab as:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eTherefore, for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"53\" height=\"18\" style=\"width: 53px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 60px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 30px; transform-origin: 442.71875px 30px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(10*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        12\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eBe careful though, in using the Matlab \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/ref/integral.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003efunction, as it is only an approximation. For example if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"74\" height=\"18\" style=\"width: 74px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 260px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 442.71875px 130px; transform-origin: 442.71875px 130px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt;\u0026gt;  s = S(100000)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eWarning: Reached the \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003elimit on the maximum number of intervals in use. Approximate bound on error is\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e8.0e+01. The integral \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003emay not exist\u003c/span\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e, or \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eit may be difficult to approximate numerically to the\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003erequested \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eaccuracy. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u0026gt; In integralCalc/iterateScalarValued (line 372)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc/vadapt (line 132)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegralCalc (line 75)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003eintegral (line 87)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eIn \u003c/span\u003e\u003cspan style=\"border-block-end-color: rgb(170, 4, 249); border-block-start-color: rgb(170, 4, 249); border-bottom-color: rgb(170, 4, 249); border-inline-end-color: rgb(170, 4, 249); border-inline-start-color: rgb(170, 4, 249); border-left-color: rgb(170, 4, 249); border-right-color: rgb(170, 4, 249); border-top-color: rgb(170, 4, 249); caret-color: rgb(170, 4, 249); color: rgb(170, 4, 249); column-rule-color: rgb(170, 4, 249); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(170, 4, 249); text-decoration-color: rgb(170, 4, 249); text-emphasis-color: rgb(170, 4, 249); \"\u003e@(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003es =\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 442.71875px 10px; transform-origin: 442.71875px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       49841\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThe correct answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"65\" height=\"18\" style=\"width: 65px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. The \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(n)\r\n    % NOTE: the following expression is inaccurate for some values of n\r\n    s = round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n)); \r\nend","test_suite":"%%\r\nn = 1:20;\r\ns_correct = [0 0 0 1 1 1 2 2 3 3 3 4 4 5 6 6 6 7 7 7];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:20).*pi;\r\ns_correct = [1 2 3 4 6 7 8 11 11 12 15 16 17 18 20 22 23 24 26 28];\r\nassert(isequal(arrayfun(@S,n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100*exp(1);\r\ns_correct = 126;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 1234.5678;\r\ns_correct = 601;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 12345.6789;\r\ns_correct = 6125;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 100000;\r\ns_correct = 49839;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 6e6;\r\ns_correct = 2998571;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 4e8*pi;\r\ns_correct = 628304194;\r\nassert(isequal(S(n),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = 10.^(1:10);\r\ns_correct = 5555500618;\r\nassert(isequal(sum(arrayfun(@S,n)),s_correct))\r\nassert(isempty(lastwarn))\r\n%%\r\nn = (1:1e5).*exp(2);\r\ns = arrayfun(@S,n);\r\nss = round([sum(s) nnz(s) mean(s) median(s) mode(s) std(s) sum(num2str(s))]);\r\nss_correct = [18444149135 100000 184441 184439 303161 106553 37072130];\r\nassert(isequal(ss,ss_correct))\r\nassert(isempty(lastwarn))","published":true,"deleted":false,"likes_count":0,"comments_count":8,"created_by":255988,"edited_by":255988,"edited_at":"2023-05-18T18:10:19.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":"2023-05-18T18:10:19.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-05-04T18:21:04.000Z","updated_at":"2023-05-18T18:10:26.000Z","published_at":"2023-05-05T19:51:12.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a postive real number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, we are asked to evaluate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=S(n)=\\\\Bigg\\\\lfloor\\\\ \\\\int_0^n\\\\sqrt{\\\\lfloor{x}\\\\rfloor} - \\\\Big\\\\lfloor{\\\\sqrt{x} \\\\Big\\\\rfloor\\\\ \\\\mathrm{d}x\\\\  \\\\Bigg\\\\rceil \\\\cdot\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            where:     the symbol \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rfloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/floor.html#\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efloor\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e function,\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                            and \\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lfloor\\\\ \\\\rceil\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e\\\" is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/round.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eround \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e(to the nearest integer) function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe may rewrite the above function in Matlab as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  S = @(n) round(integral(@(x) sqrt(floor(x))-floor(sqrt(x)),0,n));]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=10\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  s = S(10*pi)\\ns =\\n        12]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBe careful though, in using the Matlab \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/ref/integral.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003efunction, as it is only an approximation. For example if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=100000\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[\u003e\u003e  s = S(100000)\\n\\nWarning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is\\n8.0e+01. The integral may not exist, or it may be difficult to approximate numerically to the\\nrequested accuracy. \\n\u003e In integralCalc/iterateScalarValued (line 372)\\nIn integralCalc/vadapt (line 132)\\nIn integralCalc (line 75)\\nIn integral (line 87)\\nIn @(n)round(integral(@(x)sqrt(floor(x))-floor(sqrt(x)),0,n)) \\n\\ns =\\n       49841]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe correct answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=49839\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function is off by only 2 units here, but the discrepancy could be even greater for other values of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function can also be quite slow. The challenge is to find an efficient and more accurate algorithm to evaluate the integral.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52328,"title":"ICFP2021 Hole-In-Wall: Figure Validation with Segment Crossing Check","description":"The ICFP held its annual 3-day contest in July 2021 with Hole-In-Wall. Contest Specification.\r\nThe contest folds the figure in Red to fit within the hole shown in light grey \r\nThis Challenge is to evaluate the complete Figure validation defined in the Specification when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\r\nValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u003c= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.  \r\nValid=check_figureS(hxy, pxy, mseg, epsilon, npxy)  \r\nCrossing Segments appears in Cody 1720 but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\r\nThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use Register Team. Anyone can select Problems Page and then click problem numbers to see the puzzles and to download problem files.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 669px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 334.5px; transform-origin: 407px 334.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 7.91667px; transform-origin: 14px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.icfpconference.org/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eICFP\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.65px 7.91667px; transform-origin: 146.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e held its annual 3-day contest in July 2021 with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eHole-In-Wall\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.95px 7.91667px; transform-origin: 29.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Contest \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/spec-v4.1.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpecification\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 237px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 118.5px; text-align: left; transform-origin: 384px 118.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.267px 7.91667px; transform-origin: 230.267px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe contest folds the figure in Red to fit within the hole shown in light grey \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 238px;height: 237px\" 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\" data-image-state=\"image-loaded\" width=\"238\" height=\"237\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.083px 7.91667px; transform-origin: 231.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to evaluate the complete Figure validation defined in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/spec-v4.1.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpecification\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.25px 7.91667px; transform-origin: 113.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.05px 7.91667px; transform-origin: 381.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u0026lt;= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 170.667px 7.91667px; transform-origin: 170.667px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValid=check_figureS(hxy, pxy, mseg, epsilon, npxy)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.65px 7.91667px; transform-origin: 97.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCrossing Segments appears in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1720\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody 1720\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242.167px 7.91667px; transform-origin: 242.167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.883px 7.91667px; transform-origin: 375.883px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://poses.live/register\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRegister Team\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 7.91667px; transform-origin: 42.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Anyone can select \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://poses.live/problems\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblems Page\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.35px 7.91667px; transform-origin: 256.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and then click problem numbers to see the puzzles and to download problem files.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function valid=check_figureS(hxy,pxy,mseg,epsilon,npxy)\r\n% hxy hole vertices in order of connection. Last row repeats first for use in inpolygon\r\n% pxy figure original vertices used for initial segment length calculations\r\n% mseg is paired list of connected vertices\r\n% epsilon is allowed stretchiness of segment. hxy,pxy,npxy are all integer\r\n% npxy is figure final vertices used for scoring and Validation\r\n valid=0;\r\n nseg=size(mseg,1);\r\n msegMM=calc_msegMM(pxy,mseg,epsilon,nseg); %Create Min and Max segment integer values\r\n %hplot(hxy,pxy,mseg,size(mseg,1),1);\r\n %hplot3(hxy,npxy,mseg,size(mseg,1),3,segMM);\r\n \r\n%Confirm all final vertices of npxy are in hxy polygon\r\n[in] = inpolygon(npxy(:,1),npxy(:,2),hxy(:,1),hxy(:,2)); % inside or on edge\r\n%check if all vertices are in\r\n\r\n%Confirm all segments are of valid length squared\r\n for i=1:nseg\r\n  nsegL2=0; %calc length squared of segment\r\n  %Check if nsegL2\u003cMin or nsegL2\u003eMax  Min=msegMM(i,1) and Max=msegMM(i,2)\r\n end\r\n \r\n%Confirm all figure segments do not cross hole segments\r\n%Segment/Hole Vertices may touch other vertices and segments\r\n%Intersecting Segments was addressed in Cody 1720\r\n%https://www.mathworks.com/matlabcentral/cody/problems/1720\r\n%A Robust/Fast solution for 1720 was created on 7/18/21 of size 117\r\n \r\n valid=check_intersecting_segments(hxy,mseg,nseg,npxy);\r\nend % check_figure\r\n\r\nfunction valid=check_intersecting_segments(hxy,mseg,nseg,npxy)\r\n%Confirm no figure segments cross hole segments; \r\n % Allowed: \r\n % a) Overlaying segments. \r\n % b) Segments touching hole vertices.\r\n % c) Figure vertices touching hole segments\r\n \r\n valid=0;\r\n nhxy=size(hxy,1)-1;\r\n \r\n for i=1:nseg\r\n  A=[]; % npxy points defined by mseg   A=[a1 a2;a3 a4]\r\n  for j=1:nhxy  %1-2,2-3, end-1 to end  thus why nhxy is 1 less than rows\r\n   B=[]; % hxy points    B=[b1 b2;b3 b4]\r\n   if intersecting(A,B), return;end % intersect detected thus fail\r\n  end\r\n end\r\n \r\n valid=1;\r\nend % check_intersecting_segments\r\n\r\nfunction tf=intersecting(A,B) %\r\n%Correct full solution requires two cross product checks which can be implemented using det\r\n%Segment A [A1;A2],  Segment B [B1;B2]\r\n% Points A1=[a1,a2] A2=[a3,a4] B1=[b1 b2] B2=[b3 b4]  All data in z=0 plane\r\n%p0= B2A1 x B2B1 is det([B2A1;B2B1]) where B2A1 = B2-A1= [b3-a1 b4-a2], B2B1=B2-B1=[b3-b1 b4-b2]\r\n%p1= B2A2 x B2B1 is det([B2A2;B2B1]) where B2A2 = B2-A2= [b3-a3 b4-a4], B2B1=B2-B1=[b3-b1 b4-b2]\r\n%p2= A2B1 x A2A1 is det([A2B1;A2A1]) where A2B1 = A2-B1= [a3-b1 a4-b2], A2A1=A2-A1=[a3-a1 a4-a2]\r\n%p3= A2B2 x A2A1 is det([A2B2;A2A1]) where A2B2 = A2-B2= [a3-b3 a4-b4], A2A1=A2-A1=[a3-a1 a4-a2]\r\n%visualization https://www.desmos.com/calculator/0wr2rfkjbk\r\n%source https://stackoverflow.com/questions/3838329/how-can-i-check-if-two-segments-intersect\r\n% by BenMan95 in ghastly Python not using det or matlab array vectors\r\n%https://www.mathworks.com/matlabcentral/cody/problems/1720\r\n%  Robust Fast solution of size 117 created on 7/18/21 for 1720\r\n%\r\n% Both cross product pair multiplications must be negative for an intersection to occur\r\n% p0p1\u003c0 \u0026\u0026 p2p3\u003c0 for non-endpoint segments intersection. For End point intersection change \u003c to \u003c=\r\n\r\ntf=0;\r\nend % intersecting\r\n\r\n\r\nfunction msegMM=calc_msegMM(pxy,mseg,epsilon,nseg)\r\n%determine Min and Max integer value of allowed length squared for each segment\r\n%abs(Lsqr(npxy,seg(i))/Lsqr(pxy,seg(i))-1)\u003c= epsilon/1000000.\r\n%mseg has indices of connected vertices [nseg,2].  The nseg may exceed number of vertices.\r\n msegMM=zeros(nseg,2);\r\n for i=1:nseg\r\n  Lseg=0; % sum((pxy(mseg(i,1),:)-pxy(mseg(i,2),:)).^2)\r\n  delta=0; % epsilon*Lseg/1000000 and a little tweak\r\n  msegMM(i,:)=[-delta delta]+Lseg;\r\n end\r\nend % calc_msegMM\r\n\r\n%These routines can be used to visualize the data\r\n\r\n% function hplot(vxy,qxy,mseg,Lmseg,id)\r\n% %Need check of segment crossing a hole segment but ignore endpoint\r\n%  [in] = inpolygon(qxy(:,1),qxy(:,2),vxy(:,1),vxy(:,2)); % inside or on edge\r\n%  figure(id)\r\n%   plot(vxy(:,1),vxy(:,2),'k.-') % hole polygon\r\n%   hold on\r\n%   plot(qxy(in,1),qxy(in,2),'b*') % points inside\r\n%   plot(qxy(~in,1),qxy(~in,2),'ro') % points outside\r\n%   for i=1:size(qxy,1)%length(xq)\r\n%    text(qxy(i,1)+.75,qxy(i,2)-1.5,num2str(i),'FontSize',12);\r\n%   end\r\n%   \r\n%   for i=1:Lmseg\r\n%    if in(mseg(i,1))+in(mseg(i,2))\u003c2\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'r-') % segment to OOB pt\r\n%    else\r\n%     plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'b-')\r\n%    end\r\n%    text(sum(qxy(mseg(i,:),1))/2,sum(qxy(mseg(i,:),2))/2,num2str(i),'Color','b');\r\n%   end\r\n%   \r\n%   %o+*.x_|sd^v\u003e\u003cph\r\n%   %colors ymcrgbwk\r\n%    \r\n%   axis tight\r\n%   axis ij\r\n%   hold off  \r\n% end % hplot\r\n\r\n% function hplot3(vxy,qxy,mseg,Lmseg,id,segMM)\r\n%  segMNM=[segMM(:,1) segMM(:,1)+segMM(:,2) segMM(:,2)];\r\n%  [in] = inpolygon(qxy(:,1),qxy(:,2),vxy(:,1),vxy(:,2)); % inside or on edge\r\n%  figure(id)\r\n%   plot(vxy(:,1),vxy(:,2),'k.-') % hole polygon\r\n%   hold on\r\n%   plot(qxy(in,1),qxy(in,2),'b*') % points inside\r\n%   plot(qxy(~in,1),qxy(~in,2),'ro') % points outside\r\n%   for i=1:size(qxy,1) %length(xq)\r\n%    text(qxy(i,1)+.75,qxy(i,2)-1.5,num2str(i));\r\n%   end\r\n%   \r\n%   for i=1:Lmseg\r\n%    d2seg=(qxy(mseg(i,1),1)-qxy(mseg(i,2),1))^2+(qxy(mseg(i,1),2)-qxy(mseg(i,2),2))^2;\r\n%    if d2seg\u003csegMNM(i,1)\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'b-') % segment too short\r\n%    elseif d2seg\u003esegMNM(i,3)\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'r-') % segment too long\r\n%    else\r\n%     plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'g-') \r\n%    end\r\n%    text(sum(qxy(mseg(i,:),1))/2,sum(qxy(mseg(i,:),2))/2,num2str(i),'Color','b');\r\n%   end\r\n%   \r\n%   %o+*.x_|sd^v\u003e\u003cph\r\n%   %colors ymcrgbwk\r\n%   \r\n%   axis tight\r\n%   axis ij\r\n%   hold off\r\n% end % hplot3\r\n%","test_suite":"%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=pxy;\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0+10\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0.001    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0; %non-integer npxy\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16+1    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[15     0\r\n    35    20\r\n    20    44\r\n     0    24\r\n    15     0];\r\npxy=[0    20\r\n    20     0\r\n    20    40\r\n    40    20\r\n    49    45];\r\nmseg=[1     2\r\n     1     3\r\n     2     4\r\n     3     4\r\n     3     5\r\n     4     5];\r\nepsilon=1250;\r\nnpxy=[20    44\r\n     0    24\r\n    35    20\r\n    15     0\r\n     6    25];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n\r\n%%\r\n% Problem 6 shifted up7,left10, 1 seg fail\r\nepsilon=150000;\r\nhxy=[164   164\r\n   121   189\r\n    71   189\r\n    28   164\r\n     3   121\r\n     3    71\r\n    28    28\r\n    71     3\r\n   121     3\r\n   164    28\r\n   189    71\r\n    96    96\r\n   189   121\r\n   164   164];\r\npxy=[36    86\r\n    36   141\r\n    36   156\r\n    41   156\r\n    46   131\r\n    51    56\r\n    56   116\r\n    56   141\r\n    66   116\r\n    71    81\r\n    71    96\r\n    71   131\r\n    71   156\r\n    86    81\r\n    86    96\r\n    86   131\r\n    86   141\r\n    86   156\r\n    91   116\r\n    96    36\r\n   101   116\r\n   106    81\r\n   106    96\r\n   106   131\r\n   106   141\r\n   106   156\r\n   121    81\r\n   121    96\r\n   121   131\r\n   121   156\r\n   126   116\r\n   136   116\r\n   136   141\r\n   141    56\r\n   146   131\r\n   151   156\r\n   156    86\r\n   156   141\r\n   156   156];\r\nmseg=[2     3\r\n     3     4\r\n     4     8\r\n     8     2\r\n     2     1\r\n     1     6\r\n     6    20\r\n    20    34\r\n    34    37\r\n    37    38\r\n    38    33\r\n    33    36\r\n    36    39\r\n    39    38\r\n    33    30\r\n    30    26\r\n    26    25\r\n    25    33\r\n     8    17\r\n    17    18\r\n    18    13\r\n    13     8\r\n    17    25\r\n    10    11\r\n    11    15\r\n    15    14\r\n    14    10\r\n    22    23\r\n    23    28\r\n    28    27\r\n    27    22\r\n     6    10\r\n    10     1\r\n    34    27\r\n    27    37\r\n     5     7\r\n     7     9\r\n     9    12\r\n    12    16\r\n    16    19\r\n    19    21\r\n    21    24\r\n    24    29\r\n    29    31\r\n    31    32\r\n    32    35\r\n    15    19\r\n    23    21];\r\nnpxy=[26    79\r\n    26   134\r\n    26   149\r\n    31   149\r\n    36   124\r\n    41    49\r\n    46   109\r\n    46   134\r\n    56   109\r\n    61    74\r\n    61    89\r\n    61   124\r\n    61   149\r\n    76    74\r\n    76    89\r\n    76   124\r\n    76   134\r\n    76   149\r\n    81   109\r\n    86    29\r\n    91   109\r\n    96    74\r\n    96    89\r\n    96   124\r\n    96   134\r\n    96   149\r\n   111    74\r\n   111    89\r\n   111   124\r\n   111   149\r\n   116   109\r\n   126   109\r\n   126   134\r\n   131    49\r\n   136   124\r\n   141   149\r\n   146    79\r\n   146   134\r\n   146   149];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\n%problem 6 with rotate/shift, 1 seg fail\r\nepsilon=150000;\r\nhxy=[164   164\r\n   121   189\r\n    71   189\r\n    28   164\r\n     3   121\r\n     3    71\r\n    28    28\r\n    71     3\r\n   121     3\r\n   164    28\r\n   189    71\r\n    96    96\r\n   189   121\r\n   164   164];\r\npxy=[36    86\r\n    36   141\r\n    36   156\r\n    41   156\r\n    46   131\r\n    51    56\r\n    56   116\r\n    56   141\r\n    66   116\r\n    71    81\r\n    71    96\r\n    71   131\r\n    71   156\r\n    86    81\r\n    86    96\r\n    86   131\r\n    86   141\r\n    86   156\r\n    91   116\r\n    96    36\r\n   101   116\r\n   106    81\r\n   106    96\r\n   106   131\r\n   106   141\r\n   106   156\r\n   121    81\r\n   121    96\r\n   121   131\r\n   121   156\r\n   126   116\r\n   136   116\r\n   136   141\r\n   141    56\r\n   146   131\r\n   151   156\r\n   156    86\r\n   156   141\r\n   156   156];\r\nmseg=[2     3\r\n     3     4\r\n     4     8\r\n     8     2\r\n     2     1\r\n     1     6\r\n     6    20\r\n    20    34\r\n    34    37\r\n    37    38\r\n    38    33\r\n    33    36\r\n    36    39\r\n    39    38\r\n    33    30\r\n    30    26\r\n    26    25\r\n    25    33\r\n     8    17\r\n    17    18\r\n    18    13\r\n    13     8\r\n    17    25\r\n    10    11\r\n    11    15\r\n    15    14\r\n    14    10\r\n    22    23\r\n    23    28\r\n    28    27\r\n    27    22\r\n     6    10\r\n    10     1\r\n    34    27\r\n    27    37\r\n     5     7\r\n     7     9\r\n     9    12\r\n    12    16\r\n    16    19\r\n    19    21\r\n    21    24\r\n    24    29\r\n    29    31\r\n    31    32\r\n    32    35\r\n    15    19\r\n    23    21];\r\nnpxy=[53   156\r\n   108   156\r\n   123   156\r\n   123   151\r\n    98   146\r\n    23   141\r\n    83   136\r\n   108   136\r\n    83   126\r\n    48   121\r\n    63   121\r\n    98   121\r\n   123   121\r\n    48   106\r\n    63   106\r\n    98   106\r\n   108   106\r\n   123   106\r\n    83   101\r\n     3    96\r\n    83    91\r\n    48    86\r\n    63    86\r\n    98    86\r\n   108    86\r\n   123    86\r\n    48    71\r\n    63    71\r\n    98    71\r\n   123    71\r\n    83    66\r\n    83    56\r\n   108    56\r\n    23    51\r\n    98    46\r\n   123    41\r\n    53    36\r\n   108    36\r\n   123    36];\r\nValid=check_figureS(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-18T21:43:20.000Z","updated_at":"2021-07-19T01:11:39.000Z","published_at":"2021-07-19T01:11:39.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.icfpconference.org/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eICFP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e held its annual 3-day contest in July 2021 with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eHole-In-Wall\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Contest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/spec-v4.1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpecification\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe contest folds the figure in Red to fit within the hole shown in light grey \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"237\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"238\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to evaluate the complete Figure validation defined in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/spec-v4.1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpecification\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u0026lt;= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValid=check_figureS(hxy, pxy, mseg, epsilon, npxy)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCrossing Segments appears in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1720\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody 1720\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://poses.live/register\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRegister Team\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Anyone can select \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://poses.live/problems\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblems Page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and then click problem numbers to see the puzzles and to download problem 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52334,"title":"ICFP2021 Hole-In-Wall: Figure Validation with Segment Crossing and Segment on Wall Checks","description":"The ICFP held its annual 3-day contest in July 2021 with Hole-In-Wall. Contest Specification.\r\nThe contest folds the figure in Red to fit within the hole shown in light grey \r\nThis Challenge is to evaluate the complete Figure validation defined in the Specification when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\r\nValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u003c= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.   4) Pathological cases of Segments crossing Wall region between Hole Vertices or from figure vertices on Hole edges is not allowed.\r\nValid=check_figureSP(hxy, pxy, mseg, epsilon, npxy)  \r\nCrossing Segments appears in Cody 1720 but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\r\nThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use Register Team. Anyone can select Problems Page and then click problem numbers to see the puzzles and to download problem files.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 690px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 345px; transform-origin: 407px 345px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14px 7.91667px; transform-origin: 14px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.icfpconference.org/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eICFP\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 146.65px 7.91667px; transform-origin: 146.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e held its annual 3-day contest in July 2021 with \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eHole-In-Wall\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.95px 7.91667px; transform-origin: 29.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Contest \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/spec-v4.1.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpecification\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.95px 7.91667px; transform-origin: 1.95px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 237px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 118.5px; text-align: left; transform-origin: 384px 118.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 230.267px 7.91667px; transform-origin: 230.267px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe contest folds the figure in Red to fit within the hole shown in light grey \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: middle;width: 238px;height: 237px\" 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\" data-image-state=\"image-loaded\" width=\"238\" height=\"237\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 126px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 63px; text-align: left; transform-origin: 384px 63px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 231.083px 7.91667px; transform-origin: 231.083px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThis Challenge is to evaluate the complete Figure validation defined in the \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://icfpcontest2021.github.io/spec-v4.1.pdf\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eSpecification\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.25px 7.91667px; transform-origin: 113.25px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 105px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 52.5px; text-align: left; transform-origin: 384px 52.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 381.05px 7.91667px; transform-origin: 381.05px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u0026lt;= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.   4) Pathological cases of Segments crossing Wall region between Hole Vertices or from figure vertices on Hole edges is not allowed.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 175.333px 7.91667px; transform-origin: 175.333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eValid=check_figureSP(hxy, pxy, mseg, epsilon, npxy)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e  \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 97.65px 7.91667px; transform-origin: 97.65px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eCrossing Segments appears in \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/1720\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eCody 1720\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242.167px 7.91667px; transform-origin: 242.167px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.883px 7.91667px; transform-origin: 375.883px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://poses.live/register\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRegister Team\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 42.7833px 7.91667px; transform-origin: 42.7833px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Anyone can select \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://poses.live/problems\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eProblems Page\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 256.35px 7.91667px; transform-origin: 256.35px 7.91667px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and then click problem numbers to see the puzzles and to download problem files.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function valid=check_figureSP(hxy,pxy,mseg,epsilon,npxy)\r\n% hxy hole vertices in order of connection. Last row repeats first for use in inpolygon\r\n% pxy figure original vertices used for initial segment length calculations\r\n% mseg is paired list of connected vertices\r\n% epsilon is allowed stretchiness of segment. hxy,pxy,npxy are all integer\r\n% npxy is figure final vertices used for scoring and Validation\r\n valid=0;\r\n nseg=size(mseg,1);\r\n msegMM=calc_msegMM(pxy,mseg,epsilon,nseg); %Create Min and Max segment integer values\r\n %hplot(hxy,pxy,mseg,size(mseg,1),1);\r\n %hplot3(hxy,npxy,mseg,size(mseg,1),3,segMM);\r\n \r\n%Confirm all final vertices of npxy are in hxy polygon\r\n[in] = inpolygon(npxy(:,1),npxy(:,2),hxy(:,1),hxy(:,2)); % inside or on edge\r\n%check if all vertices are in\r\n\r\n%Confirm all segments are of valid length squared\r\n for i=1:nseg\r\n  nsegL2=0; %calc length squared of segment\r\n  %Check if nsegL2\u003cMin or nsegL2\u003eMax  Min=msegMM(i,1) and Max=msegMM(i,2)\r\n end\r\n \r\n%Confirm all figure segments do not cross hole segments\r\n%Segment/Hole Vertices may touch other vertices and segments\r\n%Intersecting Segments was addressed in Cody 1720\r\n%https://www.mathworks.com/matlabcentral/cody/problems/1720\r\n%A Robust/Fast solution for 1720 was created on 7/18/21 of size 117\r\n \r\n valid=check_intersecting_segments(hxy,mseg,nseg,npxy);\r\n if valid==0,return;end\r\n \r\n valid=check_segments_inpoly(hxy,mseg,npxy);\r\nend % check_figureSP\r\n\r\nfunction valid=check_segments_inpoly(hxy,mseg,npxy)\r\n%Verify whole of segments are within the hole\r\n%Method: Test point along segment at distance \u003c=0.5 from segment start point\r\n valid=0;\r\n dpxy=[]; % start point for each segment\r\n %intra-segment create a point a small delta from starting point; \r\n %mid-point not sufficient\r\n dxdy=[];\r\n dxdyabsmax=[];  % Note: max has a new form of max(m,[],2) to get row max values\r\n dpxy=dpxy+dxdy./dxdyabsmax;\r\n \r\n [in] = inpolygon(dpxy(:,1),dpxy(:,2),hxy(:,1),hxy(:,2)); % inside or on edge\r\n if nnz(in==0),return;end  %nnz is fastest check of a vector all condition\r\n \r\n valid=1;\r\nend %check_segments_inpoly\r\n\r\nfunction valid=check_intersecting_segments(hxy,mseg,nseg,npxy)\r\n%Confirm no figure segments cross hole segments; \r\n % Allowed: \r\n % a) Overlaying segments. \r\n % b) Segments touching hole vertices.\r\n % c) Figure vertices touching hole segments\r\n \r\n valid=0;\r\n nhxy=size(hxy,1)-1;\r\n \r\n for i=1:nseg\r\n  A=[]; % npxy points defined by mseg   A=[a1 a2;a3 a4]\r\n  for j=1:nhxy  %1-2,2-3, end-1 to end  thus why nhxy is 1 less than rows\r\n   B=[]; % hxy points    B=[b1 b2;b3 b4]\r\n   if intersecting(A,B), return;end % intersect detected thus fail\r\n  end\r\n end\r\n \r\n valid=1;\r\nend % check_intersecting_segments\r\n\r\nfunction tf=intersecting(A,B) %\r\n%Correct full solution requires two cross product checks which can be implemented using det\r\n%Segment A [A1;A2],  Segment B [B1;B2]\r\n% Points A1=[a1,a2] A2=[a3,a4] B1=[b1 b2] B2=[b3 b4]  All data in z=0 plane\r\n%p0= B2A1 x B2B1 is det([B2A1;B2B1]) where B2A1 = B2-A1= [b3-a1 b4-a2], B2B1=B2-B1=[b3-b1 b4-b2]\r\n%p1= B2A2 x B2B1 is det([B2A2;B2B1]) where B2A2 = B2-A2= [b3-a3 b4-a4], B2B1=B2-B1=[b3-b1 b4-b2]\r\n%p2= A2B1 x A2A1 is det([A2B1;A2A1]) where A2B1 = A2-B1= [a3-b1 a4-b2], A2A1=A2-A1=[a3-a1 a4-a2]\r\n%p3= A2B2 x A2A1 is det([A2B2;A2A1]) where A2B2 = A2-B2= [a3-b3 a4-b4], A2A1=A2-A1=[a3-a1 a4-a2]\r\n%visualization https://www.desmos.com/calculator/0wr2rfkjbk\r\n%source https://stackoverflow.com/questions/3838329/how-can-i-check-if-two-segments-intersect\r\n% by BenMan95 in ghastly Python not using det or matlab array vectors\r\n%https://www.mathworks.com/matlabcentral/cody/problems/1720\r\n%  Robust Fast solution of size 117 created on 7/18/21 for 1720\r\n%\r\n% Both cross product pair multiplications must be negative for an intersection to occur\r\n% p0p1\u003c0 \u0026\u0026 p2p3\u003c0 for non-endpoint segments intersection. For End point intersection change \u003c to \u003c=\r\n\r\ntf=0;\r\nend % intersecting\r\n\r\n\r\nfunction msegMM=calc_msegMM(pxy,mseg,epsilon,nseg)\r\n%determine Min and Max integer value of allowed length squared for each segment\r\n%abs(Lsqr(npxy,seg(i))/Lsqr(pxy,seg(i))-1)\u003c= epsilon/1000000.\r\n%mseg has indices of connected vertices [nseg,2].  The nseg may exceed number of vertices.\r\n msegMM=zeros(nseg,2);\r\n for i=1:nseg\r\n  Lseg=0; % sum((pxy(mseg(i,1),:)-pxy(mseg(i,2),:)).^2)\r\n  delta=0; % epsilon*Lseg/1000000 and a little tweak\r\n  msegMM(i,:)=[-delta delta]+Lseg;\r\n end\r\nend % calc_msegMM\r\n\r\n%These routines can be used to visualize the data\r\n\r\n% function hplot(vxy,qxy,mseg,Lmseg,id)\r\n% %Need check of segment crossing a hole segment but ignore endpoint\r\n%  [in] = inpolygon(qxy(:,1),qxy(:,2),vxy(:,1),vxy(:,2)); % inside or on edge\r\n%  figure(id)\r\n%   plot(vxy(:,1),vxy(:,2),'k.-') % hole polygon\r\n%   hold on\r\n%   plot(qxy(in,1),qxy(in,2),'b*') % points inside\r\n%   plot(qxy(~in,1),qxy(~in,2),'ro') % points outside\r\n%   for i=1:size(qxy,1)%length(xq)\r\n%    text(qxy(i,1)+.75,qxy(i,2)-1.5,num2str(i),'FontSize',12);\r\n%   end\r\n%   \r\n%   for i=1:Lmseg\r\n%    if in(mseg(i,1))+in(mseg(i,2))\u003c2\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'r-') % segment to OOB pt\r\n%    else\r\n%     plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'b-')\r\n%    end\r\n%    text(sum(qxy(mseg(i,:),1))/2,sum(qxy(mseg(i,:),2))/2,num2str(i),'Color','b');\r\n%   end\r\n%   \r\n%   %o+*.x_|sd^v\u003e\u003cph\r\n%   %colors ymcrgbwk\r\n%    \r\n%   axis tight\r\n%   axis ij\r\n%   hold off  \r\n% end % hplot\r\n\r\n% function hplot3(vxy,qxy,mseg,Lmseg,id,segMM)\r\n%  segMNM=[segMM(:,1) segMM(:,1)+segMM(:,2) segMM(:,2)];\r\n%  [in] = inpolygon(qxy(:,1),qxy(:,2),vxy(:,1),vxy(:,2)); % inside or on edge\r\n%  figure(id)\r\n%   plot(vxy(:,1),vxy(:,2),'k.-') % hole polygon\r\n%   hold on\r\n%   plot(qxy(in,1),qxy(in,2),'b*') % points inside\r\n%   plot(qxy(~in,1),qxy(~in,2),'ro') % points outside\r\n%   for i=1:size(qxy,1) %length(xq)\r\n%    text(qxy(i,1)+.75,qxy(i,2)-1.5,num2str(i));\r\n%   end\r\n%   \r\n%   for i=1:Lmseg\r\n%    d2seg=(qxy(mseg(i,1),1)-qxy(mseg(i,2),1))^2+(qxy(mseg(i,1),2)-qxy(mseg(i,2),2))^2;\r\n%    if d2seg\u003csegMNM(i,1)\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'b-') % segment too short\r\n%    elseif d2seg\u003esegMNM(i,3)\r\n%      plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'r-') % segment too long\r\n%    else\r\n%     plot(qxy(mseg(i,:),1),qxy(mseg(i,:),2),'g-') \r\n%    end\r\n%    text(sum(qxy(mseg(i,:),1))/2,sum(qxy(mseg(i,:),2))/2,num2str(i),'Color','b');\r\n%   end\r\n%   \r\n%   %o+*.x_|sd^v\u003e\u003cph\r\n%   %colors ymcrgbwk\r\n%   \r\n%   axis tight\r\n%   axis ij\r\n%   hold off\r\n% end % hplot3\r\n%","test_suite":"%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=pxy;\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0+10\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0.001    41\r\n    16    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0; %non-integer npxy\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[53 0;100 22;66 68;43 68;0 41;53 0];\r\npxy=[0    48\r\n     9    34\r\n    14    34\r\n    27    41\r\n    30    53\r\n    33    68\r\n    44     0\r\n    44    58\r\n    44    63\r\n    56    68\r\n    59    53\r\n    61    41\r\n    89    21];\r\nmseg=[8     7\r\n     7     4\r\n     4     8\r\n     4     5\r\n     5     8\r\n     8     9\r\n     9     6\r\n     6     5\r\n     9    10\r\n    10    11\r\n    11     8\r\n     8    12\r\n    12    11\r\n    12     7\r\n    10    13\r\n    13     9\r\n     6     2\r\n     2     3\r\n     3     9\r\n     3     1\r\n     1     2];\r\nepsilon=40000;\r\nnpxy=[0    41\r\n    16+1    36\r\n    20    39\r\n    37    41\r\n    40    53\r\n    43    68\r\n    53     0\r\n    54    58\r\n    54    63\r\n    66    68\r\n    69    53\r\n    71    41\r\n   100    22];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nhxy=[15     0\r\n    35    20\r\n    20    44\r\n     0    24\r\n    15     0];\r\npxy=[0    20\r\n    20     0\r\n    20    40\r\n    40    20\r\n    49    45];\r\nmseg=[1     2\r\n     1     3\r\n     2     4\r\n     3     4\r\n     3     5\r\n     4     5];\r\nepsilon=1250;\r\nnpxy=[20    44\r\n     0    24\r\n    35    20\r\n    15     0\r\n     6    25];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=1;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n\r\n%%\r\n% Problem 6 shifted up7,left10, 1 seg fail\r\nepsilon=150000;\r\nhxy=[164   164\r\n   121   189\r\n    71   189\r\n    28   164\r\n     3   121\r\n     3    71\r\n    28    28\r\n    71     3\r\n   121     3\r\n   164    28\r\n   189    71\r\n    96    96\r\n   189   121\r\n   164   164];\r\npxy=[36    86\r\n    36   141\r\n    36   156\r\n    41   156\r\n    46   131\r\n    51    56\r\n    56   116\r\n    56   141\r\n    66   116\r\n    71    81\r\n    71    96\r\n    71   131\r\n    71   156\r\n    86    81\r\n    86    96\r\n    86   131\r\n    86   141\r\n    86   156\r\n    91   116\r\n    96    36\r\n   101   116\r\n   106    81\r\n   106    96\r\n   106   131\r\n   106   141\r\n   106   156\r\n   121    81\r\n   121    96\r\n   121   131\r\n   121   156\r\n   126   116\r\n   136   116\r\n   136   141\r\n   141    56\r\n   146   131\r\n   151   156\r\n   156    86\r\n   156   141\r\n   156   156];\r\nmseg=[2     3\r\n     3     4\r\n     4     8\r\n     8     2\r\n     2     1\r\n     1     6\r\n     6    20\r\n    20    34\r\n    34    37\r\n    37    38\r\n    38    33\r\n    33    36\r\n    36    39\r\n    39    38\r\n    33    30\r\n    30    26\r\n    26    25\r\n    25    33\r\n     8    17\r\n    17    18\r\n    18    13\r\n    13     8\r\n    17    25\r\n    10    11\r\n    11    15\r\n    15    14\r\n    14    10\r\n    22    23\r\n    23    28\r\n    28    27\r\n    27    22\r\n     6    10\r\n    10     1\r\n    34    27\r\n    27    37\r\n     5     7\r\n     7     9\r\n     9    12\r\n    12    16\r\n    16    19\r\n    19    21\r\n    21    24\r\n    24    29\r\n    29    31\r\n    31    32\r\n    32    35\r\n    15    19\r\n    23    21];\r\nnpxy=[26    79\r\n    26   134\r\n    26   149\r\n    31   149\r\n    36   124\r\n    41    49\r\n    46   109\r\n    46   134\r\n    56   109\r\n    61    74\r\n    61    89\r\n    61   124\r\n    61   149\r\n    76    74\r\n    76    89\r\n    76   124\r\n    76   134\r\n    76   149\r\n    81   109\r\n    86    29\r\n    91   109\r\n    96    74\r\n    96    89\r\n    96   124\r\n    96   134\r\n    96   149\r\n   111    74\r\n   111    89\r\n   111   124\r\n   111   149\r\n   116   109\r\n   126   109\r\n   126   134\r\n   131    49\r\n   136   124\r\n   141   149\r\n   146    79\r\n   146   134\r\n   146   149];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\n%problem 6 with rotate/shift, 1 seg fail\r\nepsilon=150000;\r\nhxy=[164   164\r\n   121   189\r\n    71   189\r\n    28   164\r\n     3   121\r\n     3    71\r\n    28    28\r\n    71     3\r\n   121     3\r\n   164    28\r\n   189    71\r\n    96    96\r\n   189   121\r\n   164   164];\r\npxy=[36    86\r\n    36   141\r\n    36   156\r\n    41   156\r\n    46   131\r\n    51    56\r\n    56   116\r\n    56   141\r\n    66   116\r\n    71    81\r\n    71    96\r\n    71   131\r\n    71   156\r\n    86    81\r\n    86    96\r\n    86   131\r\n    86   141\r\n    86   156\r\n    91   116\r\n    96    36\r\n   101   116\r\n   106    81\r\n   106    96\r\n   106   131\r\n   106   141\r\n   106   156\r\n   121    81\r\n   121    96\r\n   121   131\r\n   121   156\r\n   126   116\r\n   136   116\r\n   136   141\r\n   141    56\r\n   146   131\r\n   151   156\r\n   156    86\r\n   156   141\r\n   156   156];\r\nmseg=[2     3\r\n     3     4\r\n     4     8\r\n     8     2\r\n     2     1\r\n     1     6\r\n     6    20\r\n    20    34\r\n    34    37\r\n    37    38\r\n    38    33\r\n    33    36\r\n    36    39\r\n    39    38\r\n    33    30\r\n    30    26\r\n    26    25\r\n    25    33\r\n     8    17\r\n    17    18\r\n    18    13\r\n    13     8\r\n    17    25\r\n    10    11\r\n    11    15\r\n    15    14\r\n    14    10\r\n    22    23\r\n    23    28\r\n    28    27\r\n    27    22\r\n     6    10\r\n    10     1\r\n    34    27\r\n    27    37\r\n     5     7\r\n     7     9\r\n     9    12\r\n    12    16\r\n    16    19\r\n    19    21\r\n    21    24\r\n    24    29\r\n    29    31\r\n    31    32\r\n    32    35\r\n    15    19\r\n    23    21];\r\nnpxy=[53   156\r\n   108   156\r\n   123   156\r\n   123   151\r\n    98   146\r\n    23   141\r\n    83   136\r\n   108   136\r\n    83   126\r\n    48   121\r\n    63   121\r\n    98   121\r\n   123   121\r\n    48   106\r\n    63   106\r\n    98   106\r\n   108   106\r\n   123   106\r\n    83   101\r\n     3    96\r\n    83    91\r\n    48    86\r\n    63    86\r\n    98    86\r\n   108    86\r\n   123    86\r\n    48    71\r\n    63    71\r\n    98    71\r\n   123    71\r\n    83    66\r\n    83    56\r\n   108    56\r\n    23    51\r\n    98    46\r\n   123    41\r\n    53    36\r\n   108    36\r\n   123    36];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nepsilon=100000; %vertext to vertex across wall\r\nhxy=[0 0;0 2;2 2;1 1;2 0;0 0];\r\npxy=[0 0;0 2;2 2;2 0];\r\nmseg=[1 2;2 3;3 4;4 1];\r\nnpxy=[0 0;0 2;2 2;2 0];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nepsilon=100000; % mid seg connects across wall\r\nhxy=[0 0;0 4;4 4;2 2;4 0;0 0];\r\npxy=[0 0;0 4;3 3;3 1];\r\nmseg=[1 2;2 3;3 4;4 1];\r\nnpxy=[0 0;0 4;3 3;3 1];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))\r\n%%\r\nepsilon=100000; %mid seg intersect node\r\nhxy=[0 0;0 4;4 4;1 2;4 2;1 1;4 0;0 0];\r\npxy=[0 0;0 4;4 4;4 0];\r\nmseg=[1 2;2 3;3 4;4 1];\r\nnpxy=[0 0;0 4;4 4;4 0];\r\nValid=check_figureSP(hxy,pxy,mseg,epsilon,npxy);\r\nexpValid=0;\r\nfprintf('Expected Valid: %i  Valid: %i\\n',expValid,Valid);\r\nassert(isequal(Valid,expValid))","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-07-19T18:59:14.000Z","updated_at":"2021-07-19T19:33:01.000Z","published_at":"2021-07-19T19:33:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.icfpconference.org/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eICFP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e held its annual 3-day contest in July 2021 with \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eHole-In-Wall\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Contest \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/spec-v4.1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpecification\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe contest folds the figure in Red to fit within the hole shown in light grey \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"237\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"238\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis Challenge is to evaluate the complete Figure validation defined in the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://icfpcontest2021.github.io/spec-v4.1.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSpecification\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e when given the hole vertices in hxy, original figure vertices in pxy, updated figure vertices in npxy, segment matrix mseg, and epsilon. The hxy matrix is [N+1,2] where N is number of hole vertices. A repeat of the first vertex occurs for drawing the hole.  The pxy(original) and npxy(final) matrices are [P,2] where P is the number of figure vertices. The mseg indicates connected vertices that must maintain a length as a function of epsilon from the original length. The final figure vertices must be integer thus the allowed fuzziness of segment lengths.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eValid is 1) all npxy vertices must be on or inside the hole, hxy 2) all npxy segments must match the pxy segments within an allowed epsilon, abs(Lsqr(npxy,seg(i,:))/Lsqr(pxy,seg(i,:))-1)\u0026lt;= epsilon/1000000.  Lsqr is length squared 3) No figure segments may cross hole segments. Segment vertices may touch segments. No part of any Red segment should be outside the hole shown in light grey.   4) Pathological cases of Segments crossing Wall region between Hole Vertices or from figure vertices on Hole edges is not allowed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eValid=check_figureSP(hxy, pxy, mseg, epsilon, npxy)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e  \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCrossing Segments appears in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/1720\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody 1720\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e but the test set is not strong. A 7/18/21 solution of size 117 is robust and fast. See the function template for reference material to solve intersecting segments.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe ICFP 2021 Hole In Wall contest site has enabled a public user login to allow submissions. A login must be created to access all the problems and to submit solutions. Solutions are simple text files. Other challenges will show reading files, drawing figures, and producing submission files. To fully access the ICFP/Problems site use \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://poses.live/register\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRegister Team\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. Anyone can select \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://poses.live/problems\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblems Page\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e and then click problem numbers to see the puzzles and to download problem 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Sequences 110: Integration of the Sum of a Recursive Trigonometric Function","description":"A trigonometric function, , is defined as follows:\r\n                ,  in radians\r\nApplying  recursively we define another function , for integer :\r\n                \r\nWe then define  as the sum of value of  from  to :\r\n                \r\nFinally, we are asked to evaluate the integral of  with respect to , over the real range :\r\n                \r\nFor example for , , , we have:\r\n  \u003e\u003e a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\r\n       a = 7.05797686912156\r\nPlease present the final output rounded-off to 6 decimal places. Therefore the final answer is .\r\n-------------------------\r\nNOTE: There are a number of ways to do numerical Integration in Matlab.  Just make sure that the output would be accurate within 6 decimal places of the value obtained using the integral function shown above.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 507px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 462.578125px 253.5px; transform-origin: 462.578125px 253.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA trigonometric function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg 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width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"137.5\" height=\"19\" style=\"width: 137.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in radians\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eApplying \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e recursively we define another function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"46\" height=\"19\" style=\"width: 46px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, for integer \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 51px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 25.5px; text-align: left; transform-origin: 384px 25.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-20px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"166.5\" height=\"51\" style=\"width: 166.5px; height: 51px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe then define \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"44\" height=\"19\" style=\"width: 44px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e as the sum of value of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eR\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e from \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"46\" style=\"width: 129.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFinally, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ewe are asked to evaluate the integral of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eS\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, over the real range \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" 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margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-21px\"\u003e\u003cimg 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width=\"204\" height=\"48\" style=\"width: 204px; height: 48px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"42.5\" height=\"20\" style=\"width: 42.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"50\" height=\"20\" style=\"width: 50px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 40px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 459.578125px 20px; transform-origin: 459.578125px 20px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 459.578125px 10px; transform-origin: 459.578125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt; a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 459.578125px 10px; transform-origin: 459.578125px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e       a = 7.05797686912156\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"85.5\" height=\"18\" style=\"width: 85.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThere are a number of ways to do \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/help/matlab/numerical-integration-and-differentiation.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003enumerical Integration\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in Matlab.  Just make sure that the output would be accurate within 6 decimal places of the value obtained using the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003eintegral\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e function shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function a = A(n,x1,x2) \r\n    y = x;\r\nend","test_suite":"%%\r\n[n,x1,x2] = deal(1:10,pi,2*pi);\r\na_correct = [3.065357 5.25927 7.057977 8.618935 10.016842 11.294017 12.477158 13.584381 14.628646 15.619599];\r\nassert(all(abs(arrayfun(@(i) A(i,x1,x2),n)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(12,exp(1),exp(1.5));\r\na_correct = 9.752678;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(15,-2,10);\r\na_correct = 50.909769;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(25,-10*pi,0);\r\na_correct = -267.631308;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(1000,0,1000);\r\na_correct = 61793.524569;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(10000,5,1234);\r\na_correct = 244011.112390;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(123456,10000,12345);\r\na_correct = 1644471.557504;\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\n[n,x1,x2] = deal(1:1000,-pi,20*exp(1));\r\na = arrayfun(@(i) A(i,x1,x2),n);\r\ns = round([sum(a) sum(diff(a,1)) sum(diff(a,2)) sum(diff(a,3))]);\r\ns_correct = [2087798 3114 -35 7];\r\nassert(isequal(s,s_correct))\r\n%%\r\n[n,x1,x2] = deal(randi(15),rand(),100*rand());\r\nt = 'sin(atan(';\r\na_correct = 0;\r\nfor i = 1:n\r\n    a_correct = a_correct + integral(str2num(['@(x)' repmat('sin(atan(',1,i) 'x' repmat('))',1,i)]),x1,x2);\r\nend\r\na_correct = round(a_correct,6);\r\nassert(all(abs(A(n,x1,x2)-a_correct)\u003c=0.000001))\r\n%%\r\nfiletext = fileread('A.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-23T09:34:40.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-16T08:49:13.000Z","updated_at":"2023-04-23T09:34:40.000Z","published_at":"2023-04-16T17:57:39.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA trigonometric function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x) = \\\\sin(\\\\arctan(x))\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e in radians\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eApplying \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e recursively we define another function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, for integer \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}(x,n)=\\\\underbrace{\\\\text{T}(\\\\text{T}(\\\\text{T}(...\\\\text{T}(x))))}\\\\\\\\_{\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\text{n times}}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe then define \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}(x,n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e as the sum of value of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{R}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}(x,n) = \\\\sum_{k=1}^{n} \\\\text{R}(x,k) \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFinally, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ewe are asked to evaluate the integral of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{S}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, over the real range \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[x_1,x_2]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=\\\\text{A}(n,x_1,x_2) = \\\\int^{x_2}_{x_1} \\\\text{S}(x,n)\\\\ \\\\mathrm{d}x}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_1=\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex_2=2\\\\pi\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[  \u003e\u003e a = integral(@(x) sin(atan(x))+sin(atan(sin(atan(x))))+sin(atan(sin(atan(sin(atan(x)))))),pi,2*pi)\\n       a = 7.05797686912156]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ea=7.057977\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eThere are a number of ways to do \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/help/matlab/numerical-integration-and-differentiation.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumerical Integration\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in Matlab.  Just make sure that the output would be accurate within 6 decimal places of the value obtained using the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eintegral\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e function shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57983,"title":"Easy Sequences 109: Summation of Derivatives of a Trigonometric Function","description":"A trigonometric function, ,  is defined as follows:\r\n                \r\n                where:     ; and \r\n                                 is in radians.\r\nIn this problem we are asked to evaluate the following summation:\r\n                \r\n                where:     is a real number; \r\n                                 is an integer; \r\n                                 or the -th derivative of  with respect to ; and \r\n                                .\r\nFor example for  and , we have:\r\n  \u003e\u003e  syms x;\r\n  \u003e\u003e  T = (1+2*tan(x)-tan(x)^2) / (1+tan(x)^2);\r\n  \u003e\u003e  S = T/2^0 + diff(T)/2^1 + diff(T,2)/2^2;\r\n  \u003e\u003e  s = vpa(subs(S,x,2))\r\n        s = 0.10315887444431633673347091141408;\r\nPlease present the final output rounded-off to 6 decimal places. Therefore the final answer is .\r\n-------------------------\r\nNOTE: Symbolic toolbox is not available to Cody players. It is possible to do numerical differentiation in Matlab without symbolic toolbox.  Just make sure that the output would be accurate within 6 decimal places of the 'exact' value obtained using syms, as shown above.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 622px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 311px; transform-origin: 407px 311px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eA trigonometric function, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"31.5\" height=\"19\" style=\"width: 31.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e,  is defined as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 38px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 19px; text-align: left; transform-origin: 384px 19px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-14px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQsAAABMCAYAAAB6f5IyAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAABC6ADAAQAAAABAAAATAAAAACEP2i+AAAQ10lEQVR4Ae2dC9AdZXnHQ4SEmxIIpaAkBAgQDCiIgkDANCAyiC1NpXaMhRYYQTGmSGUUnJJYxSIgCNqAEvFaYHCAKgWBAhGRZCCKiBcEJFxCUCFGQCtCEvr7Jbu67uw5Z3e/syfnfN/zzPy+3fe67/7PeZ99L3uSUaPCQoFQIBQIBUKBUCAUCAVCgVAgFAgFQoFQIBQIBUKBUCAUGFAFNhjQdkezQ4HhrMBobu44OBi2giXwNXgQwkKBUCAUWKvAy/h7E7yU42nCr4ewUCAUCAXWKvB+/t4PR8E2cCz8CHQet0BYKBAKhAJrFbiLv3vktJhCWGfxPIzNpUUwFAgFRqACriGe1OK+nyN+JbieERYKhAKhQKECryTWkcW1hak9igwv1SOh4zKhwBAUOCgp+9Uh1BFFQ4Fhq4BD8lNgQsU7nEf+V1Qs0+/ZF9LAS0s0slHNYmRR4hPocZaNuN6JMKeh6/qZnwBfhutgLuwC/WYX0qCp8HjFhi0n/22wccVy/Zp9Ng0bDx47WWjWSaFhkr4h93E8LAXnpxdDt21Q9vD/nhu/FdSkjvmewoI6BfuszOG0x+/DDiXaFZqVEGm4ZNmbG3kHzIeqzmJzyrjd5qikndXdw7f+D7eruItpO1OXq/6OKuraRAo+C8fWraBNuV5pcQBt0FHslmtL0Yip3zXL3UIEu6XALCqq6iycslim0/y+7h7+FdT9DeiFXcJFruzChd5HHU28Ht0LLfai7Y+AD5CsbUHgbtgkG8l5v2uWa24Eu6VAU86izh6+6xsXgI5oERwI+SfdfsQ5fbLdkyFrTnsOA598PpGPhGNhWyiysUQ6qnCE1c7G5BK9t/yUxbbY7mm5vHWDQ9XC674KZiYNeDXHE2BGEk4P6vvLhIUcU+7g/Bn4PGStnzXLtjPOG1DATueXvMqaRdmRRVFz2+3h70OBG5L2LOP4FfggaH5Jb4QH4CT4JrwAtl87C54C7+Vj8CisTsJ2hs0gb28lYg38RT4hCbs7cg9Yz7lJnD+2Wg62b8MkzoOOyjcezzfQBRuKFlO5/iLw3u6H8yDVQn1STXVI6mRcK/YlLWv9rFm2nXHegAK9dhY+xf1ivr3FvThyMD0/DXGYb/wZoG0Nq+AhA5jrJ1eBeZ4Av+Tj4GYw7gjIm2sqv8pHZsLbcO62qOsROhyfwvfBh+BsyJtp3XyRqa4WOq49wfsWncWmYEc3fBfUtZ5plvXEdRsb5QZbgffQ/AXw9Yq34RP+Ybg7Kfc0R5/w2yXhFzk66tDmQtohruH8UJgO10PWtiewIhuRO08diSMandu3wGG9bSkyn+I7FiV0Oa6TFo4ibIumRqeuPRs16n84ek+OWl4Oz0FV65lmDnvCBkuBy2iuX6osritofiGz8Z7/rQktbDbx48FjVfsuBVyLWAxzwGG2X9zsA8inZt7sLJojhLw5Ovm/fGRB2GtrjnZaOQrTl8KWnuTsDsJ5nVqFP5orWxSsq4V1PQn2w80M1LBeafZnH2yNdkaR9aCAX0zXBrK2J4H9wc7jED1rdpgiO5zID8B0+D3UsX+k0CfhYjgM7oN0ZMFpZXuKEjuVKJVOdTpltQOuLMj0v8T9uCC+KGpJUWRBXLe1KLhEYVSvNAtnUSh/f0deSvMkaz7ZdRanwePZhBbnBxA/H3QYLqiltjEnz6eBDsejSP8i/AtcBN2wZVQyDnQ4PnGLbCyR85KEaUUZMnHjObfOvM3NRwwx3IQWZZvUK83i565lP5FhlG8v7uW/YCb8LHNfW3D+HdgkE+fpqiScH85/hHiHz99P0jfg6NTCxTzjW5nprcw1EG33dYfCv2cRezUshNeCc33XJRxd5W0PIh7MRw4h3G0tbEo7Pco0tWeatftQyzS0bp53UtCb9IPuhvmF/dduVNQHdeybtGFiA23ZjTpvBB3C+bAwwTn8Y/ADyE9Jfkqci5WvgTfBOeDWZjoCOYNzn6xfBR2KX/7Z4OhlB9B8wqc2OTlx9JC3W4hYCXlncRBxp8OpoFP4BHwb0mt9ifPfQNa2JTAVrspGDvG8G1roUDdK2mH/2yk5L9IjSWp7WG+aKfAbhsiUtrc2atTJpK+B4zvkq5I8ncx/gPOqFOqzvLvQHj/4F+AlWA2XwwzoZHPIYJkJbTL6xXw0yWfeIlJHla9mARF+ZjoSPz/NkYmLkdbzOzgRPp2EV3C8BMxvujslp8AseAaM09mcC3n7TyJuyEU6mrCMzmxckqbjUyPXaI5M4rKH9xK4PxvRpfM6Wvw1174PvAe5HXaGO5Owca6hOFKqY+tFM58S6Q3VPS5uc7f7kWZn+HibPHWT3kVBv9D/ULeCAS5nJ7wXfOI3ZZOo2DWNrDlieDVsmIm0E+enMpnkjqeOPHQAx2RyjuXcjpS9jsnbg0/qvJn/MdChNWGTqLQXWpRt+3rRLPXgOgqHeXPBp9a74WZIHYhPceN8yjh3vRyMM10PWmRbEvkIXAMbQBP271T6HOSHsU1cK+psToGjqfrX8Mqal/B7fGHNsoNarOeaXYBSdvhTCxRziJ86iwcK0l9PnKOGnxekGXUtvAgOv5oyvf1y+Als3tRFot6eKOAU5Tqo+mA5jjKLYAyMNOupZp9H3Yeh6APq5Cz8YJyn/sKTnL2TsI7G+pu22VzAa81r+kJRf+MK2PG3q3iVM8g/kh8UPdPsawhthy+yMs7ibyjoAlbebiHCDjwpn9BA2PnqU/AIFDk9osNCgVBgqApMoYJW88QyzsJpgNORrE0gsBp+lI1s+PxK6tc5zWj4OlF9KDBiFBidu1O3mpzz1zW3w5bkCs8i7HUcXZQ1V9PfBv8GRcPKtxB/DrglVWS3JpH/XJQYcaFAKNCsAmVGFkUt+DaRPuVbdex8mbOJcEfD0YjlxIWb1LLt+C2Rm6YJmeOunFvuiUxcnIYCoUCPFMh20qLdkFbNWEqCHde94DJmR3eByj10nYFlfwraKWDcF8CF2JuhyFyrWAU6nPzefFH+bJzvgqzoAjdlK43zUGAkKVDHWdhp0/cvfM+iqvlOhs5CDgOnOU5BypiLnJabWCZzJs+BSbn0unWPizN1xmkoMPAKVH3qVr1h3ygcAz7hf1O1MPlvh6OScjdydDrisYw5OtgaHKE8VqZAkufHHE+skL9V1irXbFVHxIcCfaNA085iu+ROdRQ+oavanZkCdr4zM+FOp6lzqjqisdznOlXexXRfT7+8i/VFVaFANxXwbWg3Ptr+lLgbF3R9QXNLtY7dQyGnHtr3wB8ulTV3VDTXLsJCgVCghwrUWbPQSaRz/rE12upOR7r28GTF8suSa0+tWC6yhwKhQIECTU9DHBXY2V27GA/LoYq5RuG6g7YtTIaHDJSwtJxOo4q5G3J9lQIt8joSclE2LBQYFgo07SwUyc6qs/DN0CrO4kjyu9A4H94D2kFQxlm4TuFIxmnQM1DF1GSrKgVa5C366XSLrBEdCvS/AlWcRXbdYaMKt+Y7EnuDHX1JyXJ/Sb4F4MjiP+AkcBvWOi4Dr38RnA7+lDlvBycR9+YTSoRjN6SESJElFGinwNUkpusPvmH5snaZM2lHJOW+mYnLn+q03gq7gE7pDlgEqTOz03tt1y2MuxhuBR1IkflvGZhfJxMWCoQCPVLA4fzbwPWH1Fl4/DiMg06mU3H64XQg7fz5MscTkdatI3KdY4dMpk9k0q1rRS49k3XtqaMDXwbrxnQiX3eEB1+BXbmFc8C1qUvhXdDqwUNSWBkFZpJpDaQduej49RIV+XsPyx7TIu/RSbp5nFbsn8u3I2E7v+krwelIK5tGgvkcCYWFAnkF3kKEW/B+R7J8gfBoCFvPCkzi+o4sXJxsNbpwF+IwKPphGNGjtgFHOC6WtrPbSHQUtHe7TJE2IhXw3Ztl4KjC0cXr4AJInUa7hxDZwnqlwN9xIT+UExq84CHJNU5u8BpR9eAq4A7blQXNv4I4v5tnFqRF1HpS4Dyu65rEXg1c361ZXwkvMy1q4PJR5QAoMIM2OqLI26lE6Cw+kE+I8PpTwCnId+AJ2L6Lzdicur4PP4ctulhvVDUyFPC3QDqLJh5iI0PBhu7SNyvvBLdD3Snphl1HJQ/A5G5UFnWMOAV8F+iHEDsiffjRj6FNb4durT67HvKKPrzPaFL/K+DUxKnxlBJNNU+dd3fmUS6+nyUEjizDSwHfnj0R5gyD29qSe3gQfM+ikzlqXQp7dMpYkK5e34ONC9IiKhQYdgq43uTLc3YY5/e+RTvI5ujWt4A/WuImxpLHzn5oibytstxEwoJWiREfCgwnBXxv5R0wH6o6CxegfSI7Kulk5v1wp0xDTHet7Cq4sKCeoqf/Z8lXtOVaULxl1ERSnoVjW+aIhFBgmCkwi/up6iycslhmQgktriDPN0rkq5vFRczL4EuQX9B8N3Efgay9isBq2D0bWfP8fZRz2jOQ5tAyLBToBwVc7P4UOHpZDAfC0/Az0LaCvwLf4F0Kt8ELkJqjhUPA7fNfwnQYDzfCLyA139j8J/guWEdqviG8K+yURiRHnaM7be6YtDOnNdn26Ihs06pMoW9xfhFMgzsy8XEaCgxLBew8L0GVNYsyI4t9qPOGpO5lHL8CHwTNXy77ew6nDafBClgCm4B2FjwFtutj8Cg4GjCs49gMNBcajWvF9WbK2d2EP5OLywZPIXAPeL1zk4SDOS4H72PDJM6DzsOfIpxvICwUGO4KNOUs1G0/sCPnpyGOMHxqp9OG9Pcc6S6GayGuQVj2CdgXxsHNYJzOpq79moLvbVN4G9LcFn0WdEy7wX3wITgb8mbatfnIQQhnvd4gtDfaODIVuI3bduHRjq/9cN3hj//D+ouEnSpoc+EuT7Br4FCYDkWjBqLb2qakur3qSKaV/SpJcLrju0NONWaCo40iu5/IHYsS+j0unEW/f0KD177LaLKdJmubJwE7yppsAufHgJ26nR2dJO7P0ae8DkDLfn9TR7IuZd1fpwJa3Reitl5XvNS/Ku8aiPftqKiVo7C6pfA6TwbNsmIPWtujvf2pgJ0mu9BnK/cEO7od6VnImp2nk9lpvwzbgs7iFtApNW2ug2g7rzu0/ftQ29Q/Jbp+svJPwcE5C2cxOJ/VoLT0UhoqWZtDQGdxGjyeTShx7vTjv2F7mAq/hSnQC/s9F3HNYvcOF/OlrXlJnmkd8o4nfVmHPH2ZPLovWxWNGqkKrEpu3HWC1A7l5ABwTUJHoW2x7rD2v8ZMTgsP7j4M1R6mgk7Owt2Yq2EhvBZeDq5LOKLK2x5EPJiPHIRwjCwG4VPqrza606BNXHfo6l/fZXCx8jXwJjgSFoN2MBwPPuBOB+0QeBI+BzuA5pM7tcnJyXZpRI2juyzpFm62+EEE5A+gUzgc3JWZDrPB8CzImtMoR0fHZSPjPBQYbgrswg25VvACvASr4XKYAZ3MaYhlJnTKSPoCWANOAU4Gh/gLwfJyO+wDphv+IpwJadhtVt99sKM+A+Z5Hs6FOqajccSzX66wownr/gG4TavtBuriuoyOLm+ut7jIGxYKhAItFLDj3gu+fVnGJpFp40zG0ZxPAd9pSM2pyqQ00PBxPvX/BHRcqXnulCM/OndtpWj3xfyPwUwICwVCgWGqgB19CRS9ZFX2lh2JXFg2c+QLBUKBwVXABcsn4Y01buE4yiyCMTXK9k0Rh3dhoUAo0FmBpWRxW1SnUdVc93gzuN4TFgqEAqFAKBAKhAKhQCgQCoQCoUAoEAqEAqFAKBAKhAKhQCjQawX+H0no25onE3jEAAAAAElFTkSuQmCC\" width=\"133.5\" height=\"38\" style=\"width: 133.5px; height: 38px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                where:     \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"152.5\" height=\"20\" style=\"width: 152.5px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e; and \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is in radians.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eIn this problem we are asked to evaluate the following summation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23px; text-align: left; transform-origin: 384px 23px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"142.5\" height=\"46\" style=\"width: 142.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                where:    \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is a real number; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e is an integer; \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 37px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.5px; text-align: left; transform-origin: 384px 18.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"112.5\" height=\"37\" style=\"width: 112.5px; height: 37px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e or the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ek\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-th derivative of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003eT\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e with respect to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e; and \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"91\" height=\"20\" style=\"width: 91px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eFor example for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36.5\" height=\"18\" style=\"width: 36.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, we have:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 100px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 50px; transform-origin: 404px 50px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt;  syms x;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt;  T = (1+2*tan(x)-tan(x)^2) / (1+tan(x)^2);\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt;  S = T/2^0 + diff(T)/2^1 + diff(T,2)/2^2;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e  \u0026gt;\u0026gt;  s = vpa(subs(S,x,2))\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10px; transform-origin: 404px 10px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e        s = 0.10315887444431633673347091141408;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKcAAAAkCAYAAADsMiqaAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAp6ADAAQAAAABAAAAJAAAAADDGHOQAAAJNElEQVR4Ae2ZC7BXRR3HMVHzgXmDNCwIDM0yH4yvysYyw5gyw7KcUgOyRmfMR6ZjT9FyJpxyxkltytJsikIrsxl6TCpCOuiYJSbmKJkXRSRDQMBQXvX5wPnh3sN53Xu5cpHznfnc3bP7293f+Z09u3v+d8CAVm0E2gi0EWgj0EagjUAbgTYCbQTaCLQRaCPQRqCNQP+KwPb9y50+8WYovU6EU+A48J6fgtWwuTSCji6Gv8J/oU7bYTAWTgP9GglL4Fmo02AMToJPwUdhL3gBFkF3NALj7vhs34fBGwrYn7Ifw79gHuQ1hIIxMB7GwWthBSyFbVZnc+cvwjqYAbPgf+DD/DT0VsPo4AewCux3FNRpTwxmg/bPwK9gcXatf3tAmXzJnMC2zXMlZU76OvXEZ/v8AOTHTK8XUL+Dhjn5Ei2HZfBbuBvWgG2vgYGwzel07thJKccmd/8h8gZmLZyalHcn6+pxNTjx0wdUNzk7sH8ga3MbaTzMncjfmZXfS/oayMuH7FiuODfCH8GVJx1/Etdl6qnP0d/tZNKx8vmisS3TbiHsB6HDyDwP1s2AXWCb0fu5UyefN+/Kltd1FFjnGzw6X9ng+tfYfBNOg9VgX1I3OWdmdm79b4ZUPryVYD83pxXkh4Jt/gRDILQjmfMgxv97VBSkPfXZrg4Fx7gDvlHAOZTtCqnc6mNHmZRWZPnxpPYpF2Vl20QyLbtpb3zfgjt2IkRgnKi90RwaR19Vk9PVIuymlAz488zGF2tEYuOEcEV1hS3SQxRG34OKDHJlTX2OZlPJ6FNRLMMmn7qFh0/5F1HbnSFWT48qu1v4SperTJxpFlTcrFuNwXNF8oDeU91Dw3gIVZPT81XYnVEy2JmJzeTE5nLyb0uu89npFNi3H0VNzp1NfXacfcB43gfdmUDPYa9P7izbQ5HcISImrr6veF3AHcYNT62425sSu7Mq7Oqqmjxoz5aLk/H2L+nUCRi+P1Niky92NY0VyJW3iZr4HP1cTSZ8cvX06PAdOAjKNIyKaPNkmRHllyV21+btXpUvyF17jpgIvrlyMrg6XAK7QX9UGrSHKxx0KwyVTZao723qw+rIOvED7ZGSDvXXevU68GejOh2PwS7wbzi/zrib9Y7v8w85Xw6EL8ID4Na9F+SV7iBFH3dh73Ye2uTIUDU530Qrg3g9HA0GwJ8r5sIk6K/yqzTk12yZ3HZCwyPTR2nq0zLGcFUpkuXLk4o6vz6I7U/BVflwWAibUy5A06ETinw+gfK/wN6QKp10g6gom6CLkkbdmpyulAZ1PhwFZ8OR4BnNIKyAOmmvo73Fr9SmSgNVNTnTurpJ0HTsMrumPtm+iV+vx+5bcAvsDJ6Zp8Dmvo959PlhGAmD4Ai4AdZByF1hGqTnysejMktd3YuUvoj5r/0i+41l/yTn2zJnY8mGzPdJ/pwrK7t0UttHb/GM1FT+pyXGG1fR6GOJ3VMVdnVV+hbjpdtZ2u7cxGZ2WlGQfzCx/VxB/ecpW53YxNimnu9c7erUxOeqPkZTOQvSsU/JNbg9qb+bfDp5w/TriY3HhC4a2OWq64UPWR0AY+BWL9BMWLs+V//Hc90Z9Wa1Fk/UWrxksJLsHtnldi8Vb5JL770ocJs06EWBPoWqfNKmzq/rsPkDDIZj4GsQE/KN5L8MX4W+1P10Phbug32zgSaSTsnyJq7s+uf9vgN+As6F56EDToTUz7u4bqxLsYw3w59khjRuuWUNDVz4PaHCFevCbpO3tqJdvqrJKvSRZKzOfAe5a+vDLx9gnUZgcBtEm0frGlDfxOcG3Qx4O0ZrwLHnFjQ4M6sL31Zx/Rh4LHghV/dJrruo6oPoCiwXZdZDSX/YpWX/vfCrNRQraFynaVr3dFrRB/mmPjl0d/3qpI2TeDWofWDH9bm+/+ORz49mteeGpMtfj4D+euJq709Q88HJeRUcDX6/hDZZOasmp1+VZ0VL0nFwenLdX7MGIJQ+6CiLNK1zZ+hLpT7tzkBlcbfc+lBTv5bTYFbWyCOKHy8vl/6WDbS0ZEDP0J+Fg8EX5zg4Fw4BfwFS2jy5Ppf8KQtSmNxE5mdxQToZPEM01Zb4Wvc8FjIgZfKNDt0RmT5KnZzxYWn8DiwZx20y4usK80SJXVHxnVnhEtJniwz6qMztWXVn9/EFvHB9qw0r/oQsX5n4k4dLcSp/plgIcW4oC2zaJvJHJe2ifU9Sz0hN5U8rK8BxPJbEwya7UZb5ALXxgL4b9FT6Fvc0qqKTixO7c0rsXFGir0tLbMqKv5e1nVlmkJQ39TlpUpq9lxp99kOsqX6JYdznRWWNBuYq/PL6DHwBVmZ1i0lvhAiok7WpttTX+u9w8BMwGA6C/AePW0rcxy3kncyp/Oq1nR8aHuKrVDT5i+x9IDHhjiH/3QKj9yVl6Y6VFBdmd6DU7VJduSGp/NvU58pOqHw3HA6edz1XNtH5GJ2UGc4k/XaTRtqMB2f0qV4kuox8zPSOpLy/Zn3JYmWcVuCkW7/3sxTcSlO9k4s1YP1v0oqSfCflEZt8X/kmV2W2a0mPzFW+i2vL7Sv/oE+mzJfI1cmdIa+vUGC7GfmKkutOyut83gkbX84FYBzyu4Ivvi+9/bji12lXDK6FGHc6+SF1jdL6S7iw8eMwHJROzAXL7Xxr0Xtw9EXQ7wvBYMuXwDLPSu+FvC6nwHpxsrwaiuSHx3kQtqZXgKtYmWzze9D2H+BLpPaDR8ByV/38jubHQozjOXQCDIXRENu5D3sQVKk7PrtzxJim7qS+HG+Bj8OjYPkFUCXvZSyEvf242OlLt3QD1q448hzMglXgSnINxNcV2a1CJ+LlPDCISzLMW3YCFMlArgPtbi0yoGwyrABt8hi3OVAmJ9BUiFWyk7x9eP0LKIqxW2F+HK+XwV3gEaZuq+6Jz9fTb8QiHd+ym+FQKJOT+0fgud+288GjzDBopPwNjaHVw2BHI+AAWA4PgRN2a5Qr2REwKnP+MdJ7wBeuTG+lwpVpBvgg+kLD6fRg2BuehtngqlgmV6xDoANcSX0BtPfB96VG0rnHFePhy9AJxvA/UKXjqTwWHoT7wfvra18ZolUbgTYCbQTaCLQRaCPQRqCNQBuBNgJtBNoItBFoI9BGoI1AG4E2Am0E+k8E/g9fHcH11O0sUwAAAABJRU5ErkJggg==\" width=\"83.5\" height=\"18\" style=\"width: 83.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e-------------------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eSymbolic toolbox is not available to Cody players. It is possible to do \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.unioviedo.es/compnum/labs/lab07_der_int/lab07_der_int.html\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003enumerical differentiation\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e in Matlab without symbolic toolbox.  Just make sure that the output would be accurate within 6 decimal places of the 'exact' value obtained using \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; font-weight: 700; \"\u003esyms\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, as shown above.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = S(x,n)\r\n  s = x;\r\nend","test_suite":"%%\r\nx = 1:10; n = 2;\r\ns_correct = [-1.325444 0.103159 1.239586 -1.134858 -0.29505 1.380427 -0.85387 -0.669756 1.411304 -0.504863];\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 11:20; n = 2*x;\r\ns_correct = [-0.991110 -0.481399 -0.115639 -0.691700 1.142283 1.385650 -1.377653 -1.119743 0.658705  0.078175];\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 25.25; n = 25;\r\ns_correct = 1.945253;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 100; n = 100;\r\ns_correct = -0.386110;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 0.000123; n = 123;\r\ns_correct = 0.000001;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 1234; n = 1:1000;\r\na_correct = [275 250];\r\nassert(isequal([round(sum(S(x,n))) sum(round(S(x,n)))],a_correct))\r\n%%\r\nx = 123456; n = 123456;\r\ns_correct = 0.899338;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = 123456789.10111213; n = 123456789;\r\ns_correct = -1.993727;\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nx = rand()*randi(1000); n = randi(10)-1;\r\nTs = { \r\n       @(a) (2*tan(a) - tan(a)^2 + 1)/(tan(a)^2 + 1);\r\n       @(a) (2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2)/(tan(a)^2 + 1) - (2*tan(a)*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1);\r\n       @(a) 2*tan(a)^2 - 4*tan(a) - (4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2)/(tan(a)^2 + 1) + (4*tan(a)^2*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) - (4*tan(a)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - 2;\r\n       @(a) 8*tan(a)*(2*tan(a) - tan(a)^2 + 1) - 12*tan(a)^2 - (16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2)/(tan(a)^2 + 1) + 12*tan(a)*(tan(a)^2 + 1) + (12*tan(a)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - (8*tan(a)^3*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) + (6*tan(a)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - 12;\r\n       @(a) 8*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) - (16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3)/(tan(a)^2 + 1) + 48*tan(a)^2*(tan(a)^2 + 1) - 24*tan(a)^2*(2*tan(a) - tan(a)^2 + 1) - 48*tan(a)*(tan(a)^2 + 1) + 32*tan(a)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 24*(tan(a)^2 + 1)^2 - (24*tan(a)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (32*tan(a)^3*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) + (8*tan(a)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (16*tan(a)^4*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1);\r\n       @(a) 320*tan(a)*(tan(a)^2 + 1)^2 - 160*tan(a)^2*(tan(a)^2 + 1) + 160*tan(a)^3*(tan(a)^2 + 1) - 120*tan(a)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - (272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3)/(tan(a)^2 + 1) + 40*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 64*tan(a)^3*(2*tan(a) - tan(a)^2 + 1) - 80*tan(a)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - 80*(tan(a)^2 + 1)^2 + (80*tan(a)^3*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (80*tan(a)^4*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - (32*tan(a)^5*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) - (40*tan(a)^2*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (10*tan(a)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1);\r\n       @(a) 480*tan(a)^4*(tan(a)^2 + 1) - 960*tan(a)*(tan(a)^2 + 1)^2 - 480*tan(a)^3*(tan(a)^2 + 1) - (64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4)/(tan(a)^2 + 1) + 360*tan(a)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 384*tan(a)^3*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 160*tan(a)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 32*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) + 2640*tan(a)^2*(tan(a)^2 + 1)^2 - 120*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - 160*tan(a)^4*(2*tan(a) - tan(a)^2 + 1) + 480*(tan(a)^2 + 1)^3 - (240*tan(a)^4*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (60*tan(a)^2*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - (192*tan(a)^5*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) + 128*tan(a)^2*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) + (12*tan(a)*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 192*tan(a)*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + (64*tan(a)^6*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) + (160*tan(a)^3*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1);\r\n       @(a) 11424*tan(a)*(tan(a)^2 + 1)^3 - 280*(tan(a)^2 + 1)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 224*(tan(a)^2 + 1)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 1344*tan(a)^4*(tan(a)^2 + 1) + 1344*tan(a)^5*(tan(a)^2 + 1) - 1344*tan(a)^3*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - 1120*tan(a)^4*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 7392*tan(a)^2*(tan(a)^2 + 1)^2 + 17472*tan(a)^3*(tan(a)^2 + 1)^2 - (7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4)/(tan(a)^2 + 1) + 384*tan(a)^5*(2*tan(a) - tan(a)^2 + 1) + 840*tan(a)^2*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 280*tan(a)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 1344*(tan(a)^2 + 1)^3 + (672*tan(a)^5*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (280*tan(a)^3*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) + (448*tan(a)^6*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) + 128*tan(a)*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) - 384*tan(a)^3*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) + 672*tan(a)*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (128*tan(a)^7*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) - (560*tan(a)^4*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (84*tan(a)^2*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) + 896*tan(a)^2*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + (14*tan(a)*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1);\r\n       @(a) 3584*tan(a)^6*(tan(a)^2 + 1) - 30464*tan(a)*(tan(a)^2 + 1)^3 - 3584*tan(a)^5*(tan(a)^2 + 1) - (256*tan(a)^8*(tan(a)^2 + 1) - 256*tan(a)^7*(tan(a)^2 + 1) - 15872*tan(a)*(tan(a)^2 + 1)^4 + 137216*tan(a)^2*(tan(a)^2 + 1)^4 - 49152*tan(a)^3*(tan(a)^2 + 1)^3 + 185856*tan(a)^4*(tan(a)^2 + 1)^3 - 15360*tan(a)^5*(tan(a)^2 + 1)^2 + 31616*tan(a)^6*(tan(a)^2 + 1)^2 + 7936*(tan(a)^2 + 1)^5)/(tan(a)^2 + 1) + 4480*tan(a)^4*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 1680*tan(a)^2*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) + 3072*tan(a)^5*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 448*tan(a)*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) + 128*(tan(a)^2 + 1)^3*(2*tan(a) - tan(a)^2 + 1) + 161280*tan(a)^2*(tan(a)^2 + 1)^3 - 46592*tan(a)^3*(tan(a)^2 + 1)^2 + 102144*tan(a)^4*(tan(a)^2 + 1)^2 - 560*(tan(a)^2 + 1)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 896*tan(a)^6*(2*tan(a) - tan(a)^2 + 1) - 3584*tan(a)^3*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) + 15232*(tan(a)^2 + 1)^4 + 896*(tan(a)^2 + 1)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (1792*tan(a)^6*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (1120*tan(a)^4*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - (1024*tan(a)^7*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - (112*tan(a)^2*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) + 1152*tan(a)^4*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) + (16*tan(a)*(7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) - 640*tan(a)^2*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) + (256*tan(a)^8*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) + (1792*tan(a)^5*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (448*tan(a)^3*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 3584*tan(a)^2*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 1024*tan(a)*(tan(a)^2 + 1)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 3072*tan(a)^3*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 1792*tan(a)*(tan(a)^2 + 1)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2);\r\n       @(a) 1152*(tan(a)^2 + 1)^3*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 571392*tan(a)*(tan(a)^2 + 1)^4 - 9216*tan(a)^6*(tan(a)^2 + 1) + 9216*tan(a)^7*(tan(a)^2 + 1) - 1008*(tan(a)^2 + 1)*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) - 13824*tan(a)^5*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - 8064*tan(a)^3*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 8064*tan(a)^6*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 2688*(tan(a)^2 + 1)^2*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 414720*tan(a)^2*(tan(a)^2 + 1)^3 + 1769472*tan(a)^3*(tan(a)^2 + 1)^3 - 262656*tan(a)^4*(tan(a)^2 + 1)^2 + 552960*tan(a)^5*(tan(a)^2 + 1)^2 - (353792*tan(a)*(tan(a)^2 + 1)^5 - 512*tan(a)^8*(tan(a)^2 + 1) + 512*tan(a)^9*(tan(a)^2 + 1) - 274432*tan(a)^2*(tan(a)^2 + 1)^4 + 1841152*tan(a)^3*(tan(a)^2 + 1)^4 - 371712*tan(a)^4*(tan(a)^2 + 1)^3 + 1304832*tan(a)^5*(tan(a)^2 + 1)^3 - 63232*tan(a)^6*(tan(a)^2 + 1)^2 + 128512*tan(a)^7*(tan(a)^2 + 1)^2 - 15872*(tan(a)^2 + 1)^5)/(tan(a)^2 + 1) + 2048*tan(a)^7*(2*tan(a) - tan(a)^2 + 1) + 13440*tan(a)^4*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) + 3024*tan(a)^2*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) - 39168*(tan(a)^2 + 1)^4 - 672*tan(a)*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4) + (4608*tan(a)^7*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (4032*tan(a)^5*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + (2304*tan(a)^8*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) + (672*tan(a)^3*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) - 512*tan(a)*(tan(a)^2 + 1)^3*(2*tan(a) - tan(a)^2 + 1) - 3072*tan(a)^5*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) - 10752*tan(a)^2*(tan(a)^2 + 1)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) + 4032*tan(a)*(tan(a)^2 + 1)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) + 2048*tan(a)^3*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) - (512*tan(a)^9*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) - (5376*tan(a)^6*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (2016*tan(a)^4*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 4608*tan(a)*(tan(a)^2 + 1)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 13824*tan(a)^3*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (144*tan(a)^2*(7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) + 10368*tan(a)^4*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + (18*tan(a)*(256*tan(a)^8*(tan(a)^2 + 1) - 256*tan(a)^7*(tan(a)^2 + 1) - 15872*tan(a)*(tan(a)^2 + 1)^4 + 137216*tan(a)^2*(tan(a)^2 + 1)^4 - 49152*tan(a)^3*(tan(a)^2 + 1)^3 + 185856*tan(a)^4*(tan(a)^2 + 1)^3 - 15360*tan(a)^5*(tan(a)^2 + 1)^2 + 31616*tan(a)^6*(tan(a)^2 + 1)^2 + 7936*(tan(a)^2 + 1)^5))/(tan(a)^2 + 1);\r\n       @(a) 6720*(tan(a)^2 + 1)^2*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 1428480*tan(a)*(tan(a)^2 + 1)^4 - 23040*tan(a)^7*(tan(a)^2 + 1) + 23040*tan(a)^8*(tan(a)^2 + 1) + 40320*tan(a)^6*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (1024*tan(a)^10*(tan(a)^2 + 1) - 1024*tan(a)^9*(tan(a)^2 + 1) - 707584*tan(a)*(tan(a)^2 + 1)^5 + 9061376*tan(a)^2*(tan(a)^2 + 1)^5 - 3682304*tan(a)^3*(tan(a)^2 + 1)^4 + 21253376*tan(a)^4*(tan(a)^2 + 1)^4 - 2609664*tan(a)^5*(tan(a)^2 + 1)^3 + 8728576*tan(a)^6*(tan(a)^2 + 1)^3 - 257024*tan(a)^7*(tan(a)^2 + 1)^2 + 518656*tan(a)^8*(tan(a)^2 + 1)^2 + 353792*(tan(a)^2 + 1)^6)/(tan(a)^2 + 1) + 33600*tan(a)^4*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) + 20480*tan(a)^7*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) + 5040*tan(a)^2*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4) - 512*(tan(a)^2 + 1)^4*(2*tan(a) - tan(a)^2 + 1) - 960*tan(a)*(7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4) + 12349440*tan(a)^2*(tan(a)^2 + 1)^4 - 4423680*tan(a)^3*(tan(a)^2 + 1)^3 + 16727040*tan(a)^4*(tan(a)^2 + 1)^3 - 1382400*tan(a)^5*(tan(a)^2 + 1)^2 + 2845440*tan(a)^6*(tan(a)^2 + 1)^2 - 1680*(tan(a)^2 + 1)*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4) - 4608*tan(a)^8*(2*tan(a) - tan(a)^2 + 1) - 46080*tan(a)^5*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - 16128*tan(a)^3*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) + 714240*(tan(a)^2 + 1)^5 - 5760*(tan(a)^2 + 1)^3*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + 8064*tan(a)*(tan(a)^2 + 1)*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3) + 28800*tan(a)^2*(tan(a)^2 + 1)^2*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) - (11520*tan(a)^8*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) - (13440*tan(a)^6*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) + 20480*tan(a)^3*(tan(a)^2 + 1)^2*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - (5120*tan(a)^9*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2))/(tan(a)^2 + 1) - (3360*tan(a)^4*(64*tan(a)^6*(tan(a)^2 + 1) - 64*tan(a)^5*(tan(a)^2 + 1) - 544*tan(a)*(tan(a)^2 + 1)^3 + 2880*tan(a)^2*(tan(a)^2 + 1)^3 - 832*tan(a)^3*(tan(a)^2 + 1)^2 + 1824*tan(a)^4*(tan(a)^2 + 1)^2 + 272*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) + 8192*tan(a)^6*(tan(a)^2 + 1)*(2*tan(a) - tan(a)^2 + 1) - 15360*tan(a)*(tan(a)^2 + 1)^2*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) + 46080*tan(a)^3*(tan(a)^2 + 1)*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2) - (180*tan(a)^2*(256*tan(a)^8*(tan(a)^2 + 1) - 256*tan(a)^7*(tan(a)^2 + 1) - 15872*tan(a)*(tan(a)^2 + 1)^4 + 137216*tan(a)^2*(tan(a)^2 + 1)^4 - 49152*tan(a)^3*(tan(a)^2 + 1)^3 + 185856*tan(a)^4*(tan(a)^2 + 1)^3 - 15360*tan(a)^5*(tan(a)^2 + 1)^2 + 31616*tan(a)^6*(tan(a)^2 + 1)^2 + 7936*(tan(a)^2 + 1)^5))/(tan(a)^2 + 1) + (20*tan(a)*(353792*tan(a)*(tan(a)^2 + 1)^5 - 512*tan(a)^8*(tan(a)^2 + 1) + 512*tan(a)^9*(tan(a)^2 + 1) - 274432*tan(a)^2*(tan(a)^2 + 1)^4 + 1841152*tan(a)^3*(tan(a)^2 + 1)^4 - 371712*tan(a)^4*(tan(a)^2 + 1)^3 + 1304832*tan(a)^5*(tan(a)^2 + 1)^3 - 63232*tan(a)^6*(tan(a)^2 + 1)^2 + 128512*tan(a)^7*(tan(a)^2 + 1)^2 - 15872*(tan(a)^2 + 1)^5))/(tan(a)^2 + 1) + 3072*tan(a)^2*(tan(a)^2 + 1)^3*(2*tan(a) - tan(a)^2 + 1) - 7168*tan(a)^4*(tan(a)^2 + 1)^2*(2*tan(a) - tan(a)^2 + 1) + (1024*tan(a)^10*(2*tan(a) - tan(a)^2 + 1))/(tan(a)^2 + 1) + (15360*tan(a)^7*(16*tan(a)*(tan(a)^2 + 1)^2 - 8*tan(a)^2*(tan(a)^2 + 1) + 8*tan(a)^3*(tan(a)^2 + 1) - 4*(tan(a)^2 + 1)^2))/(tan(a)^2 + 1) + (8064*tan(a)^5*(272*tan(a)*(tan(a)^2 + 1)^3 - 32*tan(a)^4*(tan(a)^2 + 1) + 32*tan(a)^5*(tan(a)^2 + 1) - 176*tan(a)^2*(tan(a)^2 + 1)^2 + 416*tan(a)^3*(tan(a)^2 + 1)^2 - 32*(tan(a)^2 + 1)^3))/(tan(a)^2 + 1) - 51840*tan(a)^4*(tan(a)^2 + 1)*(4*tan(a)^2*(tan(a)^2 + 1) - 4*tan(a)*(tan(a)^2 + 1) + 2*(tan(a)^2 + 1)^2) + (960*tan(a)^3*(7936*tan(a)*(tan(a)^2 + 1)^4 - 128*tan(a)^6*(tan(a)^2 + 1) + 128*tan(a)^7*(tan(a)^2 + 1) - 5760*tan(a)^2*(tan(a)^2 + 1)^3 + 24576*tan(a)^3*(tan(a)^2 + 1)^3 - 3648*tan(a)^4*(tan(a)^2 + 1)^2 + 7680*tan(a)^5*(tan(a)^2 + 1)^2 - 544*(tan(a)^2 + 1)^4))/(tan(a)^2 + 1) - 26880*tan(a)^2*(tan(a)^2 + 1)*(16*tan(a)^4*(tan(a)^2 + 1) - 16*tan(a)^3*(tan(a)^2 + 1) - 32*tan(a)*(tan(a)^2 + 1)^2 + 88*tan(a)^2*(tan(a)^2 + 1)^2 + 16*(tan(a)^2 + 1)^3) - 5120*tan(a)*(tan(a)^2 + 1)^3*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2) - 30720*tan(a)^5*(tan(a)^2 + 1)*(2*tan(a)^2 - 2*tan(a)*(tan(a)^2 + 1) + 2);\r\n     };     \r\ns = S(x,n);\r\ns_correct = 0;\r\nfor  i = 1:n+1\r\n    s_correct = s_correct + Ts{i}(x) / 2^(i-1);\r\nend\r\ns_correct = round(s_correct,6);\r\nassert(all(abs(S(x,n)-s_correct)\u003c=0.000001))\r\n%%\r\nfiletext = fileread('S.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-16T12:26:21.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2023-04-15T15:36:04.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-14T18:29:33.000Z","updated_at":"2023-04-16T12:26:21.000Z","published_at":"2023-04-15T14:27:33.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA trigonometric function, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e,  is defined as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}(x)=\\\\frac^{1+2\\\\tan(x)-\\\\tan^2(x)}_{1+\\\\tan^2(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                where:     \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\tan^2(x) = \\\\tan(x)\\\\cdot\\\\tan(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is in radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eIn this problem we are asked to evaluate the following summation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=\\\\text{S}(x,n)=\\\\sum_{k=0}^n \\\\frac^{\\\\text{T}^{(k)}(x)}_{2^k}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                where:    \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a real number; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is an integer; \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}^{(k)}(x)=\\\\frac{\\\\mathrm{d}^k}{\\\\mathrm{d}x^k}\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e or the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e-th derivative of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e with respect to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e; and \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\text{T}^{(0)}(x)=\\\\text{T}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, we have:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[  \u003e\u003e  syms x;\\n  \u003e\u003e  T = (1+2*tan(x)-tan(x)^2) / (1+tan(x)^2);\\n  \u003e\u003e  S = T/2^0 + diff(T)/2^1 + diff(T,2)/2^2;\\n  \u003e\u003e  s = vpa(subs(S,x,2))\\n        s = 0.10315887444431633673347091141408;]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the final output rounded-off to 6 decimal places. Therefore the final answer is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003es=0.103159\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e-------------------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eSymbolic toolbox is not available to Cody players. It is possible to do \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.unioviedo.es/compnum/labs/lab07_der_int/lab07_der_int.html\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enumerical differentiation\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e in Matlab without symbolic toolbox.  Just make sure that the output would be accurate within 6 decimal places of the 'exact' value obtained using \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esyms\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, as shown above.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":55410,"title":"Easy Sequences 70: Inflection Points of Binomial Product Function","description":"Inflection points are points along the graph curve of a function, where the curvature of the curve changes from concave to convex, or vice versa. Consider the following the following binomial product function:\r\n                                \r\nwhere the coefficient  are given by the vector, . Write a function that outputs an array of the -coordinates all of the inflections of .\r\nFor example, if :\r\n                                \r\nThe plot of the function shows 2 inflection points:\r\n                                                \r\nTherefore, the function output in this case should be: . Please present the output rounded to 4 decimal places and sorted ascending.\r\n--------------\r\nNOTE: As an added challenge, some MATLAB built-in functions are disabled.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 740.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 370.25px; transform-origin: 407px 370.25px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Inflection_point\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"font-weight: 700; \"\u003eInflection points \u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 325px 8px; transform-origin: 325px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eare points along the graph curve of a function, where the curvature of the curve changes from concave to convex, or vice versa. Consider the following the following binomial product function:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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6McZpzjvcyjVnHmmU+x6T01gWCvfVM7e0at+dZUeLpBbGvnAKV8x+e+RQkaXxqVtss9JVtCqPRFa6lSz96VUwXP8pwRJU/TPUfta8z70Gmi53VJ3AKZ7b8k+Ii+v8uz7Bo6cHM1k/k1PfxbRgVInPMd/ipOUDiJJf3Jrr7vlS/fR9ZX9t+w/NSKttvynI3BK9hG5PehbnuvLV7WSoPZY7hLnRUWaYp8i7WXoninvRS+nkJ/2bKn+5+p5iv573hqs04qa0m9++R6QISIfsx80mKEZ838YwRbdR5SufOlzXn2p1L/bu8b2kEyrwelPb8lGqzR786HmttGlAxmjNjoXJA2dWFfSzHKdRC4vl6F0ZD7nPObeu7ff3TmoXUZUW96pnNNp65qldUsvjfSZorkOyShV8Bz/nJOeq/da/fN80z4k966h36Os05miqUtNhmQpdcJz/Kc4SamzHGWUlit9vrZu9FyUdTpTVKPrORlLnRflN9U+5WQa+n3qe9HLWvLTnivV/1w9T9H/dJAkqoNp6dPnp1CJ6rLPHpT6clNkm+PZrdnoPflQS9jo0oGM6iCpa0BzAdVcxiBdUlIyyzDl9KA5FGvOPN35qHGUpsqVc9Jz+acddW7/TV9euaWRvom7bybU84sujUydvMhSq668Gkn7E0tqx0Nt2dt71JDk2nnOSc/VT63+eb56fugSj/TwjqH7tKn31pyg9nu6XKOkvxLD6yx5W9Esh0Y6uzOBaZ8YdUpyp1dNcZKExJ3lyP6oLkIFFekG1+7vWrrjB+RotcDQpWU+kZFfH2CIHvLi71P9/HHSVoaWdqd9SdRxqz2ZM9AcR2/JOc+5/M+CXuYYtPp9Tv3Pta8p+p/2R5H9d11esmfXjkC81H7TsjjNVEl3h67IITipcxxZAtWqbkvz2aON3pMPVWujS+rRbWLUHx610WOORLqEq9SopQVyKCVOS/q8R4VDy2eG4E1xDnNLuKIVFl3CFc2v7z7vKKccFDDl/d751XZ8paMypbK23JOUjlCUBHTqeN9kSftGFBSM7RkrVfBcO/fAriaoE+ta/YvUU+u9Dz7KW7InT3x0wpL2Ov7Ykk6O04ECurrMapzwnDMs50Mpt/esj6fa1UOWFMhM6aNzfWjU2IzVeTrLUxLQyYFVEHaTJS2X1Wl4qp++8pYOMEjeKU5qpI0P3bOWXYzIvAW9jMjZ4p659T/Xvqbof83MaQmzlnuSUjtfE9CVyF1z755t9J58qBobXVKfNQOZozZ6LHDRCIiP8kZHTfsKk3PixgCkla/7SpTL31vizLosSy/hKmkE6b2+CVL/13LDdqk8OUMwlF/39MQS5ykqY8sgqVbB/TSaC0xo7ZEacuJrFDzXzqfM9E3Rv0j9tHTGap1wOSnp6YSS2wPDbnBQ44TrGdV/buawZhApDdold01fN1ZP3rZaBEm1TpL4dUeqfUaqW97SAQaVXc/M0e/k2v9adjEnl37fgl5G5Gxxz9z6n2tfuUGUoTKmAyS6p2RgKMqtZZBUO8AYlXXqfXu10XvyoWptdEnd1g5kDtroIcOcTo1KwOjShb7CeIdbepiAA9UoqaZ7dZUYMyn42PdJxsDnlnBFKi26hCuSV9893klqw+aVlmoOCah9d/e5GtYuv0aIr7WkpU5zdPQtg6R0g2TJ0k/nlc769T2fKnj0CNQIe8lduldtqv5F2lZLZywNMKP9hJ55taXuYTC+hLHbHtPTpKInMObYe51H69u5KujQ97SkO344SckgUqR+WgZJaduOyqk+4sKevs3bfPoh37T+o7am1jZF2OXuqX33WdDLHLtWv8+t/5E6rtV/BR0atHvCki+ZbT1I0jJISgeeW8vZqj0onz3Z6L35UDU2urRuvZ0pZoie9Dhqo4eCpHTvRXRvxFhhpMxy0qIn03nla5+A1rr3rb/WcoW/tDR0qp7eqY4k6syUVsaa96fH6EYdgjnl9VHiks5PdaOGrDbRt6ZWef7Xqf6nyN4ySPIR7LGljZL7awPtMtcBdxVc9+uEsbE2HGnnYi0nPBrYtdC/SJ21DJLSgZ2hgNCXVHzehBv7UKnLlc6g9DnhfbMcabndoR3TUb8nGjgof3/G9a27L8m/Q6R+fMrVMkhKbcoQD5Xrhad+e0huPyFLOpF+CqI7wKAT8lQ/Y23e+62hAFVtSstk/8VS39JplUknJfa1p9yzKt8adjHSHraqlxHZW9zTSv9z7SvV5RL9V75auq22nfZLnof+7+WWIvs4x3i1DJLSvShD+qbBKS15XmKbwlC592KjJf/efKiWNnqo/roDmbIL/zliU7I2eihISht06Qh0n/DKT0taxiI7Kb6uf7V0p6W/T5S8awDfb78peBsKuryh1+7DaNHRzpmH18+UZZAt5fPGP+YMpkdjq671jO/D6Dqgkk37RKJO/VhZWgZJqV50Z1d9w6dkGQpqch1w6uz+neVzv6WxY12j7dwd1LHZipb6F21bLZ0xvdOD2L7vV6m9Rb+z5rxS/eoG8jqAY6wPkjx65oZMHbrc+rzBULvxo7HV2Wtfzpct6Zt17kykg0jar6Ny3mxJA0xTrpZBUu4bVWoLKtfYsuExHUsZqF/Rv3MMdI+uof1g3p50T9eWpEFf3/6osWe9Tpa2i9G2sAW9VNt7sSX1WdKNj1qSzulI+jlWHKRsWul/rn35O9VWxvQ/PRr7fLtX7Sa1C6ljqKPzc3Yj2g5aBkmpvvT5LT4znvqIPtP3EhNY/y8f8lcsaY+i2kVJYBkt85Zt9BF8qBobrbZzhSXZEF8W57ZV9eo2oztgIF3J+ZFZG90XJHXXOA6dJBRtdLov58ylhdP93TXwfTKNjZJGjE+J/Fu61w/UaBG8tixXziB4R6539jmxvt9n6PdaWVsGSel3Hvy7NBr5utCSviNzk6V0dLsrc64Ddgb+3YvcMspoO3e5/9wE6htdbK1/0bpq7Yyl5VAf8lcnQTSq+k5Lb7QUWZYqrgrQ5Tz7jFO6p0Z1rzrKzdTknB/nlOuo0wBNz3SdjO7esVaDJy2DJMmdlkMHvWiGRpdmS7u8u23InSg5R7q6/V96wIj06C8sjX1rKTKwk/ZJXYes2x66Azpjz3rZlraLe9NLd9LF/rWW/taSf7undHlqtOy6r4X+R9pXVP/TpWp6pjtA192bOGV7RMqpZZCkfD0/DS5pQEgDPnJktWJIK4L6BolcRzQQcZeliyxpsOjunj6gpI6H7t2qjZa8R/Cham202w7ZDc3eP2rpRZZutOSD82mcIButkxnTJdl9dZ610d0gSYJc1ZOTGrA6qCnToFKQIUXwEUJ1LEPH/bpsueOA3SF8u+U1dSS1hdK1zMNHY+Y4yWqqnN74h4yX15/awB9Z6i538mNYh36vla9lkCQZfMnWGxKBvmh/H1pil8qd64BVv9ee9EQO3phDX9rOxV+BQt9sbkv9K6mn1kGS3q0+5B2WNPqoS3sDv3Sqn7Eldi63OzfdmQNfwvYMu1H1nfvYaWRmxN85tITMf1fn/wFLenffcdtp/UWP447UU+sgSe8UFwVF4qxL+n6PpUhf7TNqvgcjrSM/zlz1/alAfirbmy2NzVY7d43M99W38nju6beuruaedf5L2cVIffs9W9FLBZpKcmQ0CCX/Q3/X1T1spaR8Y/e20v9I+3I5cvrvtlFt+8OWhtqa8uv7vZZN6yBJcsjGvd6S+jJd37SkVRNDts4HIzTo5c+7H1R7ou4Yj63aaMl8FB+qxkanhyl5f+wre1I74OcJqF1p9jm3rD63euFczYlKtQonMIru0mUitXmNPeeQao7UnUOeVnmmypuOcLfKv0U+W2SvjkWX9g0M7V9rUfZIHrkOOJKH31PDWidWpstYS943x72+b0N5T10/30o+OQaRICj3vlLWcoQ+bWlseWXuna1/V3vVLNzYmu7W74zk545TrZO0lC2KlGVLsri8W9DLdFTYZ0Y9gBk6dTLCO7dUr4X+19TpFvVfwYhmbob25EV4T73HnWPVm5YSy4a7c9ydMUtnWnLvHTrcBxv9i+S24EP5zHyq+z5gkpstGmoLIRu9ZJAkQaV0WiM4l5Pvo7dbcjRyyhr5fe2jvscOI0jl9wMl9M2ZsWVnkTIf8Z5WHXBtO1c7+oKl6LKzI9bBWJkUeOqKHjAzlJeP+JUO1Mj46zriYTOt21LuaOWx98kRzq1IaC3vWH5z28Uly9LqXT6LmR6S07dXSO9Tv3ZewYuHVsS00v/a9oX+/2IleuCT7nceco5lF6PXT+zGvtkrbHSU4HL3pTPbvgVhaMAkKlXYRi8dJKkAvkShtSPgJ3IdzQH0wEOb01qtNY42JN3nG96jhygctR5KmA3d26IDnspXMmhd/1wDFS04rZGHbw7tWwpaIs9UvnKw7rLEIMM4dTlPNSd7zmV/StpI371blWtquWqf96VeaR0PzSDUviN9rpX+T61H9P/ntdK3emaqc5xrK9joHKHlf/cBk3Qf6tCASUS6Ihu9RpCkQniH1CpQkuP4GUtafhHZmB0BuZV7/KO+NQ5BizLo/Xdayu3BSN915PqYwnRqB9yKq+/feJsVJrJPZ0qZ9/Cs7wXr8vC9PtF+qhVXOYNfJ1AabDol+736HOFofS7ddlvbxaXlb/k+BcHdA37SGQQtsYnsY4vI1Er/W9Uf+v+zWnPnOD2Ixp1j+UM6NOmhxjYMGx3RmGXv8QGTdJLAB0y0B/7SAltZbKPXCpKEWI3x240aeMu8lq3+8bd5Q6hdez+lLO6Q6yOvNScJ6Xl982TKYR9T5N/is0MfKY3K2rKda0ROS1SONqgQZen3eZ1olOqJzsM66MK/1RbJV3m1ctxa5hWRfYv3+DJjzar5DJ/PrJcO3Kh8e2DaUse3WKcRmdxRTfcf+B4l6alOR/vnRrqG/kdqZJ17+pxj36PkJx5OnfnvlgwbvU5dj721b8DED3W5yR7UvrnonuZiG7BmkLS9qtiWRH1TjEtJKCN1lyUFR91NskvJcKT3yLF7pSXtx9OySV0KfHVK4VkPUtasZ3fCdVRo39V3VP2a8p61dyuQ10CRBmp0uYM8dhrWWWN0xPL6Zy7SY9f9MASVt/sh4VoG6H8tufmfk838nqXuQRveNuSX6PjnVocxYaPnr9OaN3jQ2j1ow1dYDR3AUfOu3mcIkpqhbJqRTynnTuJp+lLLzJcduFOi/Nda5te6bOQHAQhAAAIQgAAEIACBEAGCpBCmRW/yZQXpqT5zCKDZIn3I7WJL+jZWGhj5+7Ss4VlzvJw8IQABCEAAAhCAAAQgsFUCBEnbqpl0+l9LfXyjagsp+4KgXL7dr9rn7ud3CEAAAhCAAAQgAAEI7J4AQdJ2qjA96nsrUq1x5PhWyo4cEIAABCAAAQhAAAJnlABB0nYq3vcDbUWiH5ogkokLAhCAAAQgAAEIQAACZ4oAQdKZqm4KCwEIQAACEIAABCAAAQjkCBAk5QjxOwQgAAEIQAACEIAABCBwpggQJJ2p6qawEIAABCAAAQhAAAIQgECOAEFSjtCxf9eHuj5u6TpL9x67qJQOAhCAAAQgAAEIQAACMQIESTFOW7nrPhNER3lPPXVO30h6tSV9sVpX+mXzrZQVOSAAAQhAAAIQgAAEILAKAYKkVbBXv1RB0qWWXmfpwepczp3T95i+ZcmDLoKkCTB5FAIQgAAEIAABCEDgWAQIko5Vn6WlIUgqJcb9EIAABCAAAQhAAAKHJ0CQdPgqHi0gQdLZrn9KDwEIQAACEIAABCDQQ4AgaR/NQh91vcjSVZa+aOmORmITJDUCSTYQgAAEIAABCEAAAschQJC0n7rsBjT+72gJ+vYdESRF6XEfBCAAAQhAAAIQgMCZIUCQtJ+q/v5J1Jfan49b0uEL5xWI/93Tc+kjBEkFALkVAhCAAAQgAAEIQOBsECBI2kc9KyB6xNJXLb2qocgESQ1hkhUEIAABCEAAAhCAwDEIECTtox7fZWLebul6S7c2FJkgqSFMsoIABCAAAQhAAAIQOC55MqAAAAFKSURBVAYBgqR91GPfR2TZk7SPukNKCEAAAhCAAAQgAIGdESBI2keFPWViPmbpslO61/5kT9I+6g4pIQABCEAAAhCAAAR2RoAgafsVdrmJ+ICl206i3mN/KkhqcT1smeggiL6T71rkTx4QgAAEIAABCEAAAhDYHQGCpO1X2fNMxG+cxPyA/dniG0mahfpNSzee8lX+N1t6yNKT20eChBCAAAQgAAEIQAACEJiPAEHSfGzJGQIQgAAEIAABCEAAAhDYIQGCpB1WGiJDAAIQgAAEIAABCEAAAvMRIEiajy05QwACEIAABCAAAQhAAAI7JECQtMNKQ2QIQAACEIAABCAAAQhAYD4CBEnzsSVnCEAAAhCAAAQgAAEIQGCHBAiSdlhpiAwBCEAAAhCAAAQgAAEIzEeAIGk+tuQMAQhAAAIQgAAEIAABCOyQwP8C7bdw4mko5bsAAAAASUVORK5CYII=\" style=\"width: 420.5px; height: 45px;\" width=\"420.5\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21.5px; text-align: left; transform-origin: 384px 21.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere the coefficient \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 12.5px; height: 20px;\" width=\"12.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are given by the vector, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 212.5px; height: 20px;\" width=\"212.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112.5px 8px; transform-origin: 112.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that outputs an array of the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 127px 8px; transform-origin: 127px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e-coordinates all of the inflections of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 31.5px; height: 18.5px;\" width=\"31.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 141px; height: 18.5px;\" width=\"141\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64px 8px; transform-origin: 64px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" style=\"width: 359px; height: 45px;\" width=\"359\" height=\"45\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 153.5px 8px; transform-origin: 153.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe plot of the function shows 2 inflection points:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 358.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 179.25px; text-align: left; transform-origin: 384px 179.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 96px 8px; transform-origin: 96px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                                                \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" style=\"vertical-align: baseline;width: 361px;height: 353px\" 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\" data-image-state=\"image-loaded\" width=\"361\" height=\"353\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 169px 8px; transform-origin: 169px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eTherefore, the function output in this case should be: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 117px; height: 18.5px;\" width=\"117\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003ePlease present the output rounded to 4 decimal places and sorted ascending.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 35px 8px; transform-origin: 35px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e--------------\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 242px 8px; transform-origin: 242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNOTE: As an added challenge, some MATLAB built-in functions are disabled.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function ps = inflPoints(cs)\r\n    ps = cs;\r\nend","test_suite":"%%\r\ncs = [1 1 1];\r\nps_correct = -2;\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = [1 -1 1 -1];\r\nps_correct = [-1.5811 1.5811];\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = [1 2 3 4 5];\r\nps_correct = -7.6288;\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = repmat(2,1,5);\r\nps_correct = -6;\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = repmat([1 -2],1,6);\r\nps_correct = [0.5394 10.7378];\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs = repmat([1 -1 1],1,5);\r\nps_correct = [1.1646 8.4726 10.8803];\r\nassert(isequal(inflPoints(cs),ps_correct))\r\n%%\r\ncs1 = ones(1,10); cs2 = [1 -2 -3 4 5 -6 7];\r\ncs3 = repmat([1 -4],1,3); cs4 = repmat([3 -2],1,6);\r\ncs5 = [2 4 6 -8 -9 -10]; cs6 = (1:6).*3.-2;\r\nps = sort([inflPoints(cs1),inflPoints(cs2),inflPoints(cs3),inflPoints(cs4),inflPoints(cs5),inflPoints(cs6)]);\r\nps_correct = [-30.1765 -18.6599 -17.6178 -14.2587 -5.9861 -4.6735 -1.1563 1.9772 2.8718 10.2251 19.8482];\r\nassert(isequal(ps,ps_correct))\r\n%%\r\nfiletext = fileread('inflPoints.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java') ...\r\n|| contains(filetext, 'sum') || contains(filetext, 'prod') || contains(filetext, 'if') || contains(filetext, 'for') || contains(filetext, 'while') ...\r\n|| contains(filetext, 'switch') || contains(filetext, 'try') || contains(filetext, 'assignin') || contains(filetext, 'arrayfun') || contains(filetext, 'conv') ...\r\n|| contains(filetext, 'cellfun') || contains(filetext, 'bsxfun')  || contains(filetext, 'solve') || contains(filetext, 'zero');\r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":255988,"edited_by":255988,"edited_at":"2022-09-04T10:58:02.000Z","deleted_by":null,"deleted_at":null,"solvers_count":3,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2022-09-02T17:36:31.000Z","updated_at":"2022-09-04T10:58:02.000Z","published_at":"2022-09-02T20:44:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Inflection_point\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInflection points \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003eare points along the graph curve of a function, where the curvature of the curve changes from concave to convex, or vice versa. Consider the following the following binomial product function:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x)=\\\\sum_{i=1}^{n}(x+c_1i)(x+c_2i)(x+c_3i)...(x+c_{n-2}i)(x+c_{n-1}i)(x+c_ni)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere the coefficient \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ec_i\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are given by the vector, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ecs = [c_1,\\\\ c_2,\\\\ c_3,\\\\ ...\\\\ c_{n-2},\\\\ c_{n-1},\\\\ c_n]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that outputs an array of the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e-coordinates all of the inflections of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ecs=[1,\\\\ -1,\\\\ 1,\\\\ -1]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(x)=\\\\sum_{i=1}^{4}(x+i)(x-i)(x+i)(x-i) = 4x^4-60x^2+354.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe plot of the function shows 2 inflection points:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"353\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"361\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTherefore, the function output in this case should be: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[-1.5811,\\\\ 1.5811]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ePlease present the output rounded to 4 decimal places and sorted ascending.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e--------------\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: As an added challenge, some MATLAB built-in 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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52973,"title":"Easy Sequences 45: Second Derivative of Inverse Polynomial Function","description":"The inverse of a function, is the function , that reverses . That means that if , then . For example, the function to convert celsius temperature to fahrenheit is: , the inverse function (convert from fahrenheit to celsius) is: . So that,  and .\r\nGiven a polynomial function  (presented as vector of numbers), and a value , if , write a program that evaluates , where . \r\nFor example, if , and , then  and . Therefore .\r\nNOTE: It is possible for  to return some complex numbers. We are interested only with real values, so in cases where there are no real , please output an empty vector. Also please round-off your output to 4 decimal places, and sorted in ascending order.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 299.5px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 149.75px; transform-origin: 407px 149.75px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 77px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 38.5px; text-align: left; transform-origin: 384px 38.5px; white-space: pre-wrap; margin-left: 4px; 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height: 18.5px;\" width=\"32.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, is the function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 19.5px;\" width=\"44\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.5px 8px; transform-origin: 47.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, that reverses \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ef\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 63px 8px; transform-origin: 63px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. That means that if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 58.5px; height: 18.5px;\" width=\"58.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 70.5px; height: 19.5px;\" width=\"70.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.8667px 8px; transform-origin: 15.8667px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the function to convert celsius temperature to fahrenheit is: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 97.5px; height: 28px;\" width=\"97.5\" height=\"28\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 112px 8px; transform-origin: 112px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the inverse function (convert from fahrenheit to celsius) is: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 121px; height: 28px;\" width=\"121\" height=\"28\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30.5px 8px; transform-origin: 30.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. So that, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 88px; height: 18.5px;\" width=\"88\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMgAAAAnCAYAAABKSgfJAAAEn0lEQVR4nO2c0ZXjIAxFXw/uwA2kganAFaSDdOAOtoXU4BLcw7SQGtLC7AfWWnHASIhJcFb3HP/MGAuEBEJAAMdxHMdxHMdxHMdxHCEnADOAP++uiOO0RA9gBHAH8IMyB7kA6GpW6g30AIZ3V8Jpjx7BuEeUOcgVwLl2pd7EiNAepyG+jE9fqR4lDnJFmD0kUH1PynpxyJk1aOVe8ZlOUqK7Hqv+SuSVlv3HCcEo6bkjrANmALfN/1J/f5eDjEt99ugQjO0Hz+2UOhYQ2kjfkRi6Ve6Mz5kVtboDQttvACassyrpLudklrJPXJaKT3g29Blrx26N9rz8/VsrcAeNg3wh75w91nVN6snJihl6rpNryD0t36g1+LyDEt2BldnqiGx1RtrQLWWjTIiPwh0eGxZbPH5HKmJB4yAz8mEIzXZ8JD7hudNSC+NhqdOA0FZpJ1vlElfkZ8hWKdUdGfINcUOmQTtmI5aySX4SHxvw2JkxZtTNukgdRDJ7DAgjcKpDSBbNntK65Tq5plxqp2XN1AJS3XXIZzIpctl+y1I2SY90nPuHfSw1im0rshdSSEIMqYNMyId2E/ZjfT5D3jPf4nXLKbe23BuOv2CX6u7C3ksNvD3iNmQpWwSfFkdhGU3mK6YoiYN0gneAYFS5+J2m3JoOUlsuLTCPjFR33Ob2dEgzxa1SWTXb9cerpniJg1DoVyO0I0OVxPnSTq4tl0bGI4dZUt1JZ1aePCJnsJRVw9cfrxy9JA5C75hy2wuUrpakXWs6iEYurUNKUr58H8DyWE8oSHTHtxs0Rj4YyxbBsy2SBWwtaN2z5yAT0kkDDRSP3iAbSWo5iFYuOYg0zOXwOlse64Ag0d0Xyoz8YixbBN8ILP6Ign6RQ/HhHWHEjBkQNdAKdZq0fbUcRCsXy/slC/Uz1s1dy2Pdi9E6SG5Q5t/bOoi2rBq+0jfFab9EDQehlKBmj6GGg5TIBeTrlVbROkiurTzDunUQbVk1PFdsWun/EjUchNLEmti6hoOUyAX+PwdpOsTi648W8+9WB7kgOL7WyK0OUipXmtZumd/MYtH3LGVV8DNELd5NIAcugQ6xlSjG4iAWuZZF+pGyWMC69pUaOT+rZikrZnuyt8ULSKVpXouRcrlaB7HKJQcpGayOlMUCHqMXyUzDT1NYyorh2/Wtxrwl+wID8kZ6wv6IUuIgNeWWJEuOlMUCHtcSqf7lgzhfQ1jKiqE9htIp/VXcIY/J6dj43ozTIYwoNR2kltwJbSZLNGh0lztlQFmo2IldS9kskuPtrXCFzGjISL8ROin13JCfMTWdXFNu64OVBI3u+F2a7bv8xG5s4LGUzbK9q9DybTaaTvcaSkYqjbP3BoQej5unewZbUy6l3Fvbi9Kg0R1BOuTXBnqsBxL3dGYpG2XEemlq+4xo11FyF6ZSbYo9E+JTbo8wLcfKpO7C15DL23jU9G6J7jjd8g7pk64RSAYLS9mPgabTGocWW4QuXrWYSXQOwhllO9OtQ/Hypzq/80I+8XekZrQb2joH5IzPcZJP+hE8pyFqHIl4Nz2OfXPQcRzHcRzHcRzHcRzHzl/mz/9+bAB3+AAAAABJRU5ErkJggg==\" style=\"width: 100px; height: 19.5px;\" width=\"100\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 58px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 29px; text-align: left; transform-origin: 384px 29px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 99.5px 8px; transform-origin: 99.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a polynomial function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 167px 8px; transform-origin: 167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e (presented as vector of numbers), and a value \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 10.5px 8px; transform-origin: 10.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 91.5px; height: 19.5px;\" width=\"91.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 29.5px 8px; transform-origin: 29.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, write a program that evaluates \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEAAAAAlCAYAAADyUO83AAACkElEQVRoge2Z65GqQBBGTw5kYAIkQARGYAZmYAamYAyEQA6mYAymsPcHfGUzzqPBwbtbxamiat2BoeebfjnCzs7Ozv+jBY4V5zsBTcX5NqUFBuoarDnbinNyADrHtWQhLXBf+MySuR9UFOEAnIEn8BNcA+NC9Lmn7NLNNFdXy8AIHRsIfGG+eDt5x1ygc2aeAbjVNCxBD1xrTmgFGCLjJzP+ZPSckG4aj43V5jC9q5qnWVe/RMYb5h4SC4Vv7b59X19jonBxqQRj7zkFYy1pYbZCXvmxxx2Zu3eMlrxIV95zx9YoDHI5yYWMV6aP0ZPPEffpWkrLu2gqvR6eVAiDB2nXhjGuNf4gvsspYSwNY3658co51uPCcuzJJ8Nk02rkRlaAjjEsrszF6YkvXuERS54hHfOKo0VKlGPwzlJIDdN9q7HlTbtoDbhT7sFV/jwCwDzndIxCWzfWojw7KzFXJ0Ib21qAFcXTcS0VQDnnyWvHLQoDT6MjAVb3AzbmOsf/YywVQPF/572psiHpWdRHAoSlzWITXykZLREglnMs54Q9KT4qv/ZlYQa34jwLL9CiPAKE4RWikPSWto+SoB5OGV8qjxZPGYR5zol1nAo9b3Ojb6yrKLW/1kNKO+Ktx1pgzGiF0pKs7u0X3vC0v2G85oySWJ5ymdphxbOEbMkLrzAteWcU2/7mXMi6bM4tJVbOGNsAxcRUyF0ZF1fKPRfHPVE0uafWe84BxEA+D9jyF0M2Paa/S8deD1a4/4WXofa6kd49e1+fua90IKI5Us+fjC2lHKBTqm8cviziiq8afModf+P1VRpe3x+2Ql78a2mofHRt2OREeAsa6v+IscWPLZvSUPf3gW+eN+7s7Oz8ff4BzOcnAeflCJYAAAAASUVORK5CYII=\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 28px 8px; transform-origin: 28px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, where \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 74px; height: 37px;\" width=\"74\" height=\"37\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 74.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 37.25px; text-align: left; transform-origin: 384px 37.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example, if \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 189.5px; height: 19.5px;\" width=\"189.5\" height=\"19.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 20px 8px; transform-origin: 20px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, then \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg 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src=\"data:image/png;base64,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\" style=\"width: 186.5px; height: 37.5px;\" width=\"186.5\" height=\"37.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 37.5px 8px; transform-origin: 37.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 208.5px; height: 18.5px;\" width=\"208.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eNOTE: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51px 8px; transform-origin: 51px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eIt is possible for \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 293.5px 8px; transform-origin: 293.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e to return some complex numbers. We are interested only with real values, so in cases where there are no real \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 32px; height: 18.5px;\" width=\"32\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311px 8px; transform-origin: 311px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, please output an empty vector. Also please round-off your output to 4 decimal places, and sorted in ascending order.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = R(P,n)\r\n  y = x;\r\nend","test_suite":"%%\r\nP = [3 -7 2]; n = 5;\r\nr_correct = [-0.0077 0.0077];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 2 0]; n = 1;\r\nr_correct = [-0.0884 0.0884];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 2 3 4]; n = 5;\r\nr_correct = [-0.0696];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 -10 35 -50 25]; n = 1;\r\nr_correct = [-0.2500 -0.1019 0.1019 0.2500];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = 10:-2:2; n = -3;\r\nr_correct = [];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 -5 -10 -10 -5 1]; n = 0;\r\nr_correct = [-0.0458 0.0000 0.0400];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = ones(1,25); n = 1;\r\nr_correct = [-2.0000 0.1667];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = repmat([7 -2 3],1,1000); n = 4;\r\nr_correct = [-0.0785 0.0000 0.0001 0.0445];\r\nassert(isequal(R(P,n),r_correct))\r\n%%\r\nP = [1 -3 -3 1]; ns = -10:0.1:10;\r\ns = arrayfun(@(n) sum(abs(R(P,n))),ns);\r\nss = round([sum(s) median(s) mean(s) std(s)],4);\r\nss_correct = [60.5806 0.0202 0.3014 1.8229];\r\nassert(isequal(ss,ss_correct))\r\n%%\r\nfiletext = fileread('R.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":6,"test_suite_updated_at":"2021-11-01T04:59:49.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-10-24T05:55:27.000Z","updated_at":"2026-03-24T13:06:02.000Z","published_at":"2021-10-30T16:02:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Inverse_function\\\"\u003e\u003cw:r\u003e\u003cw:t\u003einverse of a function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, is the function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef^{-1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, that reverses \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. That means that if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef(a)=b\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ef^{-1}(b)=a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the function to convert celsius temperature to fahrenheit is: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(x) = \\\\frac_{9}_{5}x+32\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the inverse function (convert from fahrenheit to celsius) is: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT^{-1}(x) = \\\\frac_{5}_{9}(x-32)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. So that, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(100)=212\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT^{-1}(212)=100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a polynomial function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e (presented as vector of numbers), and a value \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ(x)=P^{-1}(x)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, write a program that evaluates \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, where \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)=\\\\frac{\\\\mathrm{d^2Q} }{\\\\mathrm{d} x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = [3\\\\ -7\\\\ 2]=3x^2-7x+2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en=5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, then \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eQ(x)=P^{-1}(x) = \\\\frac{7}{6} \\\\pm \\\\frac{\\\\sqrt{12 x + 25}}{6}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(x)=\\\\frac{\\\\mathrm{d^2Q} }{\\\\mathrm{d} x^2}=\\\\pm\\\\frac{6}{\\\\left(12x+25\\\\right)^{3/2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(n) = R(5) \\\\approx [-0.0077\\\\ 0.0077]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOTE: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eIt is possible for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e to return some complex numbers. We are interested only with real values, so in cases where there are no real \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eR(n)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, please output an empty vector. Also please round-off your output to 4 decimal places, and sorted in ascending order.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":54750,"title":"Find the length of stream affected by a spill","description":"When a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration  is often computed as a function of time  and distance  from the spill using the advection-dispersion equation:\r\n\r\nwhere  is the mean velocity of the river and  is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass  mixed over the cross section (with area ) at , the concentration can be shown—using some of the math needed for Cody Problem 51625—to be\r\n\r\nWrite a function to compute the length of stream affected by the spill. In other words, find the position  (say) beyond which the concentration never exceeds a threshold . ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 282.7px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 141.35px; transform-origin: 407px 141.35px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378.317px 8px; transform-origin: 378.317px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eC\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 123.675px 8px; transform-origin: 123.675px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is often computed as a function of time \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003et\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 8px; transform-origin: 1.94167px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and distance \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 168.833px 8px; transform-origin: 168.833px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e from the spill using the advection-dispersion equation:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 36.6px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.3px; text-align: left; transform-origin: 384px 18.3px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-16px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"dC/dt + U dC/dx = K d^2C/dx^2\" style=\"width: 126.5px; height: 36.5px;\" width=\"126.5\" height=\"36.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 21.0083px 8px; transform-origin: 21.0083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003ewhere \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eU\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 113.958px 8px; transform-origin: 113.958px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is the mean velocity of the river and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eK\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 202.158px 8px; transform-origin: 202.158px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eM\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 125.242px 8px; transform-origin: 125.242px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e mixed over the cross section (with area \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eA\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 12.05px 8px; transform-origin: 12.05px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e) at \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = 0\" style=\"width: 36.5px; height: 18px;\" width=\"36.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59.5083px 8px; transform-origin: 59.5083px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the concentration can be shown—using some of the math needed for \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/51625\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"text-decoration-line: underline; \"\u003eCody Problem 51625\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5583px 8px; transform-origin: 22.5583px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e—to be\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 40.1px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 20.05px; text-align: left; transform-origin: 384px 20.05px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\" style=\"width: 204.5px; height: 40px;\" width=\"204.5\" height=\"40\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 44px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22px; text-align: left; transform-origin: 384px 22px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 313.617px 8px; transform-origin: 313.617px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"x = L_a\" style=\"width: 42.5px; height: 20px;\" width=\"42.5\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 44.3417px 8px; transform-origin: 44.3417px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e (say) beyond which the concentration never exceeds a threshold \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-6px\"\u003e\u003cimg src=\"data:image/png;base64,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\" alt=\"C = C_t\" style=\"width: 46px; height: 20px;\" width=\"46\" height=\"20\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 8px; transform-origin: 3.88333px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function La = affectedReach(U,K,M,A,Ct)\r\n% La = length of affected reach of stream [L]\r\n% U  = mean velocity [L/T]\r\n% K  = dispersion coefficient [L^2/T]\r\n% M  = mass of contaminant [M]\r\n% A  = cross-sectional area (L^2)\r\n% Ct = threshold concentration (M/L^3)\r\n\r\n  La = M/(Ct*A);\r\nend","test_suite":"%%\r\nM = 100;                    %  Mass (kg)\r\nA = 30;                     %  Cross-sectional area (m2)\r\nU = 0.3;                    %  Mean velocity (m/s)\r\nK = 2;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 50;                     %  Mass (kg)\r\nA = 15;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 8.4;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.001;                 %  Target concentration (kg/m3)\r\nLa_correct = 26332.1;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 0.003;                 %  Target concentration (kg/m3)\r\nLa_correct = 91.59;         %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 15;                     %  Mass (kg)\r\nA = 25;                     %  Cross-sectional area (m2)\r\nU = 0.25;                   %  Mean velocity (m/s)\r\nK = 11;                     %  Dispersion coefficient (m2/s)\r\nCt = 3e-4;                  %  Target concentration (kg/m3)\r\nLa_correct = 7256.28;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 70;                     %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.15;                   %  Mean velocity (m/s)\r\nK = 1;                      %  Dispersion coefficient (m2/s)\r\nCt = 0.01;                  %  Target concentration (kg/m3)\r\nLa_correct = 1329.62;       %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%%\r\nM = 280;                    %  Mass (kg)\r\nA = 21;                     %  Cross-sectional area (m2)\r\nU = 0.54;                   %  Mean velocity (m/s)\r\nK = 3.7;                    %  Dispersion coefficient (m2/s)\r\nCt = 0.007;                 %  Target concentration (kg/m3)\r\nLa_correct = 42140.42;      %  Length of affected reach (m)\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_correct)\u003c1e-2)\r\n\r\n%% Approximately plug flow\r\nM = 5*rand;                 %  Mass (kg)\r\nA = 40;                     %  Cross-sectional area (m2)\r\nU = 0.3*(1+rand);           %  Mean velocity (m/s)\r\nK = rand*1e-3;              %  Dispersion coefficient (m2/s)\r\nCt = 0.02*rand;             %  Target concentration (kg/m3)\r\nLa_approx = (U/(4*pi*K))*(M/(Ct*A))^2;\r\nassert(abs(affectedReach(U,K,M,A,Ct)-La_approx)/La_approx\u003c1e-3)\r\n\r\n%%\r\nfiletext = fileread('affectedReach.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'assert') || contains(filetext,'switch') || contains(filetext,'regexp') || contains(filetext,'if'); \r\nassert(~illegal)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":1,"created_by":46909,"edited_by":46909,"edited_at":"2022-06-14T05:04:44.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2022-06-14T05:04:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2022-06-14T04:57:20.000Z","updated_at":"2022-06-14T05:04:44.000Z","published_at":"2022-06-14T04:59:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhen a contaminant is spilled into a stream, one might want to know how much of the stream is affected—e.g., the length over which the concentration exceeds a specified threshold. The concentration \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is often computed as a function of time \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003et\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and distance \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e from the spill using the advection-dispersion equation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"dC/dt + U dC/dx = K d^2C/dx^2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{\\\\partial C}{\\\\partial t} + U \\\\frac{\\\\partial C}{\\\\partial x} = K \\\\frac{\\\\partial^2 C}{\\\\partial x^2}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"U\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eU\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is the mean velocity of the river and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"K\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eK\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is a dispersion coefficient, which describes spreading by several mechanisms. For an instantaneous spill of mass \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"M\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e mixed over the cross section (with area \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"A\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eA\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e) at \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = 0\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = 0\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the concentration can be shown—using some of the math needed for \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/51625\\\"\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eCody Problem 51625\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e—to be\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = (M/(A sqrt(4 pi K t))) exp(-(x-U t)^2/(4 K t))\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = \\\\frac{M}{A\\\\sqrt{4\\\\pi K t}} \\\\exp\\\\left(-\\\\frac{(x-U t)^2}{4 K t}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute the length of stream affected by the spill. In other words, find the position \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"x = L_a\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex = L_a\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e (say) beyond which the concentration never exceeds a threshold \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003cw:attr w:name=\\\"altTextString\\\" w:val=\\\"C = C_t\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eC = C_t\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52562,"title":"Easy Sequences 6: Coefficient sums of derivatives","description":"Consider the polynomial function  and its first-order derivative . The sums of the coefficients of P and P', are  and , respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows:  etc.  The total sum of this sequence converge to .\r\nFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, . Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 191px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 98px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the polynomial function \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"163\" height=\"20\" style=\"width: 163px; height: 20px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and its first-order derivative \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"129.5\" height=\"35\" style=\"width: 129.5px; height: 35px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. The sums of the coefficients of P and P', are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"120\" height=\"18\" style=\"width: 120px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"108\" height=\"18\" style=\"width: 108px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"90\" height=\"18\" style=\"width: 90px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e etc.  The total sum of this sequence converge to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAJKADAAQAAAABAAAAJAAAAAAqDuP8AAACUElEQVRYCe2WT0tWQRTGrwVZQRGYiwhpVQgZSbRp4cLy3bmxPkCt8iO4zhZt/ABGBEbbWrboCxS4UIsUiWphtIhIzEQLsvo915mXc+fOa9BBV/fAc+f8mfOcw9y5c6coGmlWoFmBvV2Brn/QHyU+Cs6BM+ArWAJPwCbYTTy5Wd5xvJ/BL/AcPAZvwB8gfwt0Ek9ulvMmXhVeBQNmhlb0DlDsOxgEqXhyU67SPshzHajoROmpPg5gLgLF71dDhSe3pBJ5KhdwHAvOD2kQ+zd4FfxDSdyTW1LlGjptilw0ulVPBUPNWfHkWp6Krib0OoRvwBbBLPT1/ASKPwJWPLmWp6bHr0lF34I+M2MKXX5t+LPGH1VPbuSojVfw/AAqHIvfRn8Y7HeM50FOPLk5vrbvBlp8NbExjdPgcHtWXvHk5hmDd5jRNiNdh+JIiO82eHKzvNq82rRqQr8J29g2tl5hJ/HkZjmP430B1MQMOALuATUSG5N+HaTiyU252vYDNBXWj7S77d15VV9CTPFPSVxTPbnKr8klPDrwVHCyFi0KxTdCXHPGzBxPbkmTO6kvE+kKRWZNsajOoej6EcWeRZ7cki/X0IlYiVGHX06eGaf2UhRPbsmRa+hlZGfsN7pVV4yxbHRPrqGpqocw14H2x2ugK0Uqd3EovgZ6TNCTa2jq6jVcW0BFn4KTIMotlHiC60ROxZObclXsq1gLQE1pn7wH2lOy50ELdJL/zo1fUydi+XXp0pfUCz4C/f11cUvvQrhq4smtkTWOZgWaFWhWYD9W4C/P++GDxZTKPgAAAABJRU5ErkJggg==\" width=\"18\" height=\"18\" style=\"width: 18px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"98.5\" height=\"19\" style=\"width: 98.5px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function totSum = tot_dCoefSum(coef)\r\n  y = x;\r\nend","test_suite":"%%\r\ncs = [5 6 -7 -8];\r\nts = '88';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [3 15 -2 1];\r\nts = '120';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [-7 22 43 6 -75 3 1 0 -80 10 5];\r\nts = '-42698751';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = 1:25;\r\nts = '1836856501837772435875025';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = repmat([2,-1],1,15);\r\nts = '47298214022376392514505945712317';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = [ones(1,20) zeros(1,10)];\r\nts = '24893912605687593731774059567276';\r\nassert(isequal(tot_dCoefSum(cs),ts))\r\n%%\r\ncs = repmat([-2,-25,1],1,10);\r\nts = '-68761759219969440143678420163128';\r\nassert(isequal(tot_dCoefSum(cs),ts))","published":true,"deleted":false,"likes_count":3,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":16,"test_suite_updated_at":"2021-08-17T17:53:33.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-08-16T19:00:56.000Z","updated_at":"2025-11-30T19:39:34.000Z","published_at":"2021-08-17T12:43:32.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the polynomial function \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\\\\left(x\\\\right)=5x^3+6x^2-7x-8\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and its first-order derivative \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\frac{dP}{dx}=15x^2+12x-7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. The sums of the coefficients of P and P', are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5 + 6 - 7 - 8 = -4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e15+12-7= 20\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively. If we keep summing up coefficients for all higher derivatives the sums sequence will be as follows: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e-4,\\\\ 20,\\\\ 42, ...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e etc.  The total sum of this sequence converge to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e88\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this exercise, you are given an array corresponding to the coefficients of a polynomial function. In the example above, the coefficient array is therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[5\\\\ 6\\\\ -7\\\\ -8]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Your task is to find the total of the sum of the coefficients of the given polynomial function plus the sum of the coefficients of its first derivative plus the sum of cefficients of all its higher degree derivatives.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":57874,"title":"Easy Sequences 107: Minimized Circumcircle-Incircle Areas Ratio of Partial Pythagorean Triangles","description":"We define a Partial Pythagorean Triangle (PPT) as a right triangle wherein the hypotenuse and at least one leg are integers. Thus, the triples  and  represent a PPT, while ,  and  do not.\r\n\r\nGiven the limit , find the area of the PPT with perimeter  , such that the ratio of the areas of the triangle's circumcircle to its incircle, ,  is as small as possible.\r\n                                                              \r\nPlease present the answer rounded-off to the nearest integer.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 427px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 213.5px; transform-origin: 407px 213.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 50px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 25px; text-align: left; transform-origin: 384px 25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWe define a Partial Pythagorean Triangle (PPT) as a right triangle wherein the hypotenuse and at least one leg are integers. Thus, the triples \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62\" height=\"19\" style=\"width: 62px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"79.5\" height=\"21\" style=\"width: 79.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e represent a PPT, while \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ8AAAAqCAYAAACtHIkmAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAn6ADAAQAAAABAAAAKgAAAACjyinoAAAHWklEQVR4Ae2ad6wVRRSHUUGaICBGBJEnECEELNhRamwgEAsxChIxEo0xqNEYEyR5aCxgARX/sBKMLzFgQ8Uoyj8QC7GBilgioKCRGkBRFBD9fmHnuSzbZu/eu9f35iTf29mZM2fOnp2ddl+TJk5cBFwEXARcBFwEGloEjuaBjm1oD+Wep/oj0AoXf4YF1e+q87ChReBmHuifEilbTA4qm2VnuOgIHIoDq2EvdC3BGddHSgheY616HQ+uUW9SYw2Ae+5iItCUZlfBemhZjAvJrcpJG2mD8tUwELqBhvQB4KS6InAl7nSHO2BnmVzTdPwutIYfYCk8CzsgdxmJxV9BQ7kauhFOAifVFYGDcWclbIHDyuxaL+xPg7WgfrEVLoRcZRDW/gQ1MB30gDZSg/IM6GhTqYy68v8qmFjGNooyPYaG9Z5qYxzoQdl4eBBmgWKhvKyiUXA2qN1toE6Zm2g4leF1oF1UWumK4pOwC1S/JxQp6nRXwNcgf+qgockyHmg7tA95sGbk1YJ5H4qBnzncHwJZpC2V1oPsPZLFQFSd1zyjb0QpBPK7cP84/AX+hyuq8+nLvAy+DPjT0DrfRd7z3c81TJ4m0/8+wtKvomMzwPjbWeTZTxVX2+lTnSmNPIaS5v+JsCdNhTLrDMe+phktGdJ+QGV2qSzmp2D1D5gZYv088vQ+voJzQbvgdnAB6KM0cjGJ882N5VVtS7QRzU3MyDcvg8UV1DFfWM8M9fOuYtZE8qkub+MF2htG23qmqClvIWU/wVEQFHXE78G8p7DOG6wTdm/VT2xHvrAGk/J2JClUuLza/Mnr8TXqaS2nTURQtOsdArfDBgiKjmPu8mUO9qXLlqxE5yub885wfQR01joU5oD+kSAo3clYAnEz1zJfpVynTZ/d/ZJpO58W7E4qEwGzI7VZd92Ja1pb68wtTL4gU2u+v8MKvTwdpRlZbRLlvDZNaTzr9juleafmRUBHU3PhLPgG+oDWYXHSn8IR8DysiVNMKKvxlc/3pW2SSb7uZyvtyNfCq+X/OvYz5G5KjoB+GdDU18+z1JurflVKkskoaJq8L0kxoXyUV6414SsJulHFZmQ9MkrBNl+L1c2gXj3JtjL6S726ql8Nu129ZPkiqmm3+wn+jIPBnm/ybzHEiUZGdby4tVxcfVPWisRGUJuXm8wM14c8G/oZNu2sGtmMDDzhGdzEtVukZnSB63zRsYkq+YgCdQRxepQS+ZpqpXNijE6aoumeHU35pUhnKuusTz7NzmqoLxU1yulrlKG1kPUBXecjeJai0UdxF1GjWg/KtMko9dD8VGzsBnX4llCqDMLAtyDfV4COcMxSgmS8aGfr//Jk5Jz4KrGlrvPFhie0UBu81aDYq4MdB0F5igyVnxEssLg/Bl0dzayCThb1klRHoiDfDB8kVQiW9yGjFvSTmhaSUb8XUhQrrvPFhieyUDOPeXn6udIv2hXrvSzyZ1qm9Y8A2uCo84V1bktz9epTSMlvbU5vgyMgs4ylpgnCmRmsuM6XIWhUaQ1bQLHXrzIdwMijJJQ/xGRYXjW9LobNoEEmL9FZoukrI/IyusEzqqHeVlzns43Yf/r3kDQvc7KXrd9mtah/z7u3vTSjwpugHelpMZUnUBa32Qmr+gCZ8lcjaqKkPedb7llqk2jxQAWtIdOKhv9rIOvmJk07Nv7oRWn9MgY0ElVaZtGgpleJpuHmcCto5LoXbEXvuw6GwWj4GMJEmwadcmwPK4zJ6+WVrY3RqS/SUUoa0fwtSdtZ92nv++v/L4oW/oJA+hTuFQx1Dq0xr4XnIG9J64/afRlGeQ58xnUoaMSolGjG0XHKROgEN8EN8Cm8BTaiuGrm0k76F5jgwaVe9H77wQnwPmjXmkW0e85NrP5VxmtVO7ZbwEwbuj4MGk3CxCxUjf7KMKUS87pT/3MwbWwibb7WoGm9iF0+XdXRi6u09KbBvWB81vXSDE7MCNjw2wtLj8/QRpZ+ktiMrdFpWNQiOeyhtpOv85+gaDPzG5g6Gv2yjLRBu7rvAusg+BLVlvLWwPUQlBfJMP7oOjWoUKH712nH+KHYaRSzkbNRNvXTXLeir6ndVmz7SSr7ZTEa0nI78rT70iblu5DyIrKOp9FxoJc2tggHaFNrMNNpivIhzaNb9ZO8RpY0jqXR2YbS73AyzIFqEH0EA0HHEgsKcmgJ7WqHuhDmFuRDmmZtR+Q0NpvMR0tf3kuptLMrabGr6fEdyDLsZ285vKY+zpmgD2J0uIrL9UVAH4j6yTxfXmQy7chndruHR1rKp+BtzMjx4bAzH5MlWdEu8xLQmknrLifxEWjjFasD5ia1WJJBnTn1zc3qgYZqDswqNKctrXco1IP/T+M1uLoL1E/uhtxE53M6g5Ph5TAAnLgImAjoXFD9Qv1jGbSHXKUz1l6APaBGVsFUcNJ4I6Cf0/QfK7tBs2IddIRUkmV30hXL/aEGtBB/Bpw0zgjobLQ5/AgfwkZw4iLgIuAi4CLgIuAiUH0R+BcS0M3LFqS7RwAAAABJRU5ErkJggg==\" width=\"79.5\" height=\"21\" style=\"width: 79.5px; height: 21px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-10px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"67\" height=\"29\" style=\"width: 67px; height: 29px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"62\" height=\"19\" style=\"width: 62px; height: 19px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e do not.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 61px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 30.5px; text-align: left; transform-origin: 384px 30.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven the limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: STIXGeneral, STIXGeneral-webfont, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003eP\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration-line: underline; \"\u003earea of the PPT\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e with perimeter \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"26.5\" height=\"18\" style=\"width: 26.5px; height: 18px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e , such that the ratio of the areas of the triangle's circumcircle to its incircle,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"36\" height=\"40\" style=\"width: 36px; height: 40px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e is as small as possible.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 238px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; 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data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003ePlease present the answer rounded-off to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function A = areaPPT(P)\r\n  y = x;\r\nend","test_suite":"%%\r\nP = 20;\r\nA_correct = 12;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 50;\r\nA_correct = 72;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 100;\r\nA_correct = 420;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 500;\r\nA_correct = 2450;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 1000;\r\nA_correct = 28561;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 5000;\r\nA_correct = 485112;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 10000;\r\nA_correct = 2827442;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 50000;\r\nA_correct = 16479540;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 123456;\r\nA_correct = 642216964;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 1234567;\r\nA_correct = 36092590380;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 12345678;\r\nA_correct = 36092590380;\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 123456789;\r\nA_correct = 35239028445009;\r\nassert(abs(areaPPT(P)-A_correct)\u003c=0.01)\r\n%%\r\nP = 987654321;\r\nA_correct = '36028897335524829';\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 12345678910;\r\nA_correct = '2319322204054392180';\r\nassert(isequal(areaPPT(P),A_correct))\r\n%%\r\nP = 1e7:2e6:1e8;\r\nA = arrayfun(@areaPPT,P);\r\nS = round([mean(A) median(A) mode(A) std(A)]);\r\nS_correct = [27586216302698 35239028445009 35239028445009 14680639085634];\r\nassert(isequal(S,S_correct))\r\n%%\r\nfiletext = fileread('areaPPT.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'assignin') || contains(filetext, 'evalin');\r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":255988,"edited_by":255988,"edited_at":"2023-04-10T18:10:39.000Z","deleted_by":null,"deleted_at":null,"solvers_count":1,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2023-04-02T12:05:10.000Z","updated_at":"2026-03-13T20:20:14.000Z","published_at":"2023-04-10T18:09:16.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe define a Partial Pythagorean Triangle (PPT) as a right triangle wherein the hypotenuse and at least one leg are integers. Thus, the triples \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{3,\\\\ 4,\\\\ 5\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1,\\\\ \\\\sqrt{3}, \\\\ 2\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e represent a PPT, while \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{1,\\\\ 1,\\\\ \\\\sqrt{2} \\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{\\\\frac^{3}_5,\\\\ \\\\frac^{4}_5,\\\\ 1\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\{{4.\\\\ 4,\\\\ 4\\\\}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e do not.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003earea of the PPT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e with perimeter \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\le P\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e , such that the ratio of the areas of the triangle's circumcircle to its incircle,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left(\\\\frac^{A_c}_{A_I}\\\\right)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e is as small as possible.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                                              \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"232\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"256\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease present the answer rounded-off to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.jpeg\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.jpeg\",\"contentType\":\"image/jpeg\",\"content\":\"data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/4REARXhpZgAATU0AKgAAAAgABAE7AAIAAAASAAAISodpAAQAAAABAAAIXJydAAEAAAAkAAAQ1OocAAcAAAgMAAAAPgAAAAAc6gAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFJhbW9uIFZpbGxhbWFuZ2NhAAAFkAMAAgAAABQAABCqkAQAAgAAABQAABC+kpEAAgAAAAM2OQAAkpIAAgAAAAM2OQAA6hwABwAACAwAAAieAAAAABzqAAAACAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA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