# Three implicit terms in function

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Makrand Chaudhari on 22 Aug 2020
Answered: Ayush Gupta on 26 Aug 2020
I have a 6*6* matrix whose value is equal to zero having three symbolic variables. Laplace operator was used such as s=+j*omg and s=-j*omg.
I am getting two values of detrminants equal to zero as follow where omg, tau and g are symbolic variables and have many values. So I have to calculate multiple roots and find the values for each tau, g, omg such that g and tau are not equal to zero. So that I can plot graph of any two terms.
BB = [(1/(3060513257434037/1125899906842624)^(omg*tau*1i)*(415471748849251781954970538364364750141971222886921968877913815034103432230921157463443783955775488000000000000*g*omg^2 - (3060513257434037/1125899906842624)^(omg*tau*1i)*omg^3*14416868914402420241003611474318273084006220897994068051895406217840020735923525505334100096046141852876800000i + 153597163097383768917367315384135787927784997750594923001462905536925266721629647298782932557748093197484032000*(3060513257434037/1125899906842624)^(omg*tau*1i)*omg^4 + (3060513257434037/1125899906842624)^(omg*tau*1i)*omg^5*1020089796904656734398285362073408091468317363995185418719672833901083874571318776893238288500520281702400i - 3034381761051861338003128535472243811511596733016943404548037797001864849499992165140975749805899434164224*(3060513257434037/1125899906842624)^(omg*tau*1i)*omg^6 - (3060513257434037/1125899906842624)^(omg*tau*1i)*omg^7*20138564401186169183029907761753332619108713350320921427946365490743678057071014432158535417856819200i + 18234171715502937192873222171870623248454505078072876437760102455689841714551172835868519597064253888*(3060513257434037/1125899906842624)^(omg*tau*1i)*omg^8 + (3060513257434037/1125899906842624)^(omg*tau*1i)*omg^9*120754023534137043695102734031600801099271089601224819533868856436917062711769136844552469970275i - 815655102533801021902264952870131350812385933753890237185774758250530342027773798586835218015*(3060513257434037/1125899906842624)^(omg*tau*1i)*omg^10 - (3060513257434037/1125899906842624)^(omg*tau*1i)*omg^11*3156623583759484531072146569974352953042792841242974833079681960393770303236589309952000i + 8801092109510664108267766067039578056141400755845539512174201699431408092997222400000*(3060513257434037/1125899906842624)^(omg*tau*1i)*omg^12 - 2170283945562694887224147982022591710596991471706572360086672958818047374670706508032874667750322951788953600000000*(3060513257434037/1125899906842624)^(omg*tau*1i)*omg^2 + g*omg^3*206895362016434127335186075749450233497402414136033348958811734844246962828967896651574869072281600000000i - 214235712397832948539558443582919426441018806180816869738833483894637504956073211043999522139588788224000000*g*omg^4 - g*omg^5*106678880606199282947799258056993076520520561649699416339075206043061307366147660114328936880537600000i + 15158730466533731898353025174186179591927852176337941036669713768225053479126903772805742540619776000000*g*omg^6 + g*omg^7*7545826795347200818861531013730433072549203597339557654598927330593867831447609386276067737600000i - 299270187424941919479901835049386500533504971079931117500011987386055460876113222746863828992000000*g*omg^8 - g*omg^9*148826527152342255940060357998100005507429083077643983781713318270480366325293809401856000000i + 1794609525704694192283486135159142431037879552512514698928166517155777043046329346949120000000*g*omg^10 + g*omg^11*889667844788438324018621409757919153157657992704388809370188608689490633991127040000000i - 48093399505522754689987792716063268066346452217735188591115856281045945863372800000000*g*omg^12 + (3060513257434037/1125899906842624)^(omg*tau*1i)*omg*27958966383092401136602350960523636561666395079908910387602897859845160389832286845179828974949236736000000000000i + 4208728815842920551203851553631014918938168487844519544733266946295467768499231325104685531472005693440000000000000000*(3060513257434037/1125899906842624)^(omg*tau*1i)))/170141183460469231731687303715884105728000000000 == 0;
(2235132896710765910645820482519568583342843307045330919230224470621400785190484709146882706521837*omg^4)/2475880078570760549798248448000000 - (2353026568689486037527593979772274865180786123195987936004438047350172823842642060577617*omg^2)/184467440737095516160 + (omg^3*125046404779470719118395732486605518817056160469446020772546891516169467183819444822593i)/1475739525896764129280000 - (omg*5384701057131374486576229828254667391691487766883516980292364263325375i)/32768 - (omg^5*4750163279961127482346656555651724764464038256533376028387215146334301096253650155352606850213i)/792281625142643375935439503360000000 - (1446905975843363446237148540245172410732076994427177145265597246647770333051677782602775454428624837*omg^6)/81129638414606681695789005144064000000000 + (omg^7*24583208497541710428503305373234048607310441101465968539973590686942966378260515664256024680001i)/207691874341393105141219853168803840000000 + (284908933054733393638644096435478488257101641844888694340001600870153776789862075560445618704128967*omg^8)/2658455991569831745807614120560689152000000000 - (omg^9*4830160941365481747804109361264032043970843584048992781354754257476682508470765473782098798811i)/6805647338418769269267492148635364229120000000 - (163131020506760204380452990574026270162477186750778047437154951650106068405554759717367043603*omg^10)/34028236692093846346337460743176821145600000000 + (omg^11*770660054628780403093785783685144763926463096006585652607344228611760327938620437i)/41538374868278621028243970633760768000000 + (78169400814604231693285694744584706726987739563177544185760951651*omg^12)/1511157274518286468382720000 + (20004237053892677648718391384339415945657377238630058491724603816375*(3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^2)/8192 - ((3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^3*49808246632786000992762879263839193142004051636800643614627087i)/40960 - (2835386044991579579976157434869644832772960525980751469726781270920775455112259*(3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^4)/2251799813685248000 + ((3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^5*7059416144504578172980220606588367533239007917933050030090205642878735483i)/11258999068426240000 + (6574051401575230516354409425379663915008718051848921845535919029305151356816713*(3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^6)/73786976294838206464000 - ((3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^7*16362403609429533978646329207764789187365587515070401485471374084042115569i)/368934881474191032320000 - (1063221288521780818853918884234795784967903994839599297606056848714414758476157*(3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^8)/604462909807314587353088000 + ((3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^9*528738038782500495713848771110932053955725546777145438361292371604635201i)/604462909807314587353088000 + (41784009097718964151187942716273070104370814573776784793663921699760878529547*(3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^10)/3961408125713216879677197516800 - ((3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^11*20714193694024307746873735677402446818483481013783924499763841943104999i)/3961408125713216879677197516800 - (427155195708219845318501064178058506704851035864358164949513397*(3060513257434037/1125899906842624)^(omg*tau*1i)*g*omg^12)/1511157274518286468382720 + 12665182584745801536344831545209892720594326964207655782573139791242421875/512 == 0]
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### Answers (1)

Ayush Gupta on 26 Aug 2020
The Symbolic toolbox can be used to solve for such questions. Refer to the following documentation of Symbolic toolbox, it might help.
After solving the equation, we can get the relation between two terms using the condition where two variables cannot be zero. Once the condition is acquired, the graph can be plotted using the fplot function in MATLAB. Refer to the documentation of fplot, it also contain some example on how to use it.
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