Problem 44262. Multivariate polynomials - overload multiplication

Created by Andrew Newell

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{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Problems</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array\"><w:r><w:t>44260</w:t></w:r></w:hyperlink><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials\"><w:r><w:t>44261</w:t></w:r></w:hyperlink><w:r><w:t> work with a monomial representation of multivariate polynomials. This has two parts, a matrix</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>exponents</w:t></w:r><w:r><w:t> with a row of exponents for each monomial, and a column vector</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>coefficients</w:t></w:r><w:r><w:t> with a coefficient for each monomial.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>It would be nice to define polynomials so they can be multiplied using simple notation:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[p = p1*p2;]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This can be done by</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html\"><w:r><w:t>defining a class</w:t></w:r></w:hyperlink><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>mPoly</w:t></w:r><w:r><w:t> with two properties,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>exponents</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>coefficients</w:t></w:r><w:r><w:t>, and two methods: a</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html\"><w:r><w:t>constructor</w:t></w:r></w:hyperlink><w:r><w:t> with the syntax</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[p = mPoly(exponents, coefficients)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>and a method</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes&amp;s_tid=doc_srchtitle\"><w:r><w:t>mtimes</w:t></w:r></w:hyperlink><w:r><w:t> for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Problems <a href = "https://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array">44260</a> and <a href = "https://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials">44261</a> work with a monomial representation of multivariate polynomials. This has two parts, a matrix <tt>exponents</tt> with a row of exponents for each monomial, and a column vector <tt>coefficients</tt> with a coefficient for each monomial.It would be nice to define polynomials so they can be multiplied using simple notation:<pre class="language-matlab">p = p1*p2;
</pre>This can be done by <a href = "https://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html">defining a class</a> <tt>mPoly</tt> with two properties, <tt>exponents</tt> and <tt>coefficients</tt>, and two methods: a <a href = "https://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html">constructor</a> with the syntax<pre class="language-matlab">p = mPoly(exponents, coefficients)
</pre>and a method <a href = "https://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes&s_tid=doc_srchtitle">mtimes</a> for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.

Problems <https://www.mathworks.com/matlabcentral/cody/problems/44260-multivariate-polynomials-convert-monomial-form-to-array 44260> and <https://www.mathworks.com/matlabcentral/cody/problems/44261-sort-multivariate-monomials 44261> work with a monomial representation of multivariate polynomials. This has two parts, a matrix |exponents| with a row of exponents for each monomial, and a column vector |coefficients| with a coefficient for each monomial.

It would be nice to define polynomials so they can be multiplied using simple notation:

p = p1*p2;

This can be done by <https://www.mathworks.com/help/matlab/matlab_oop/user-defined-classes.html defining a class> |mPoly| with two properties, |exponents| and |coefficients|, and two methods: a <https://www.mathworks.com/help/matlab/matlab_oop/class-constructor-methods.html constructor> with the syntax

p = mPoly(exponents, coefficients)

and a method <https://www.mathworks.com/help/matlab/ref/mtimes.html?searchHighlight=mtimes&s_tid=doc_srchtitle mtimes> for multiplying two polynomials. You can assume that the polynomials being multiplied have the same number of variables.

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18 Solutions
7 Solvers

Last Solution submitted on Dec 30, 2020

Last 200 Solutions

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Solution 1267206

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1 Comment

Peng Liu on 13 Sep 2017

The output of * operator in this solution is a struct, rather than a mPoly object. Nevertheless, the test suite does not check the type of the output.

Solution 1234926

2 Comments

2 Comments

Andrew Newell on 20 Jul 2017

L Y Cao, since you're such a wizard with indices, I'd love to see you solve this without converting to the array form. It would be interesting to compare the approaches.

LY Cao on 21 Jul 2017

Andrew Newell, thanks for your advice.

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