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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Last Solution submitted on Jul 26, 2023

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Christian Schröder on 26 Jul 2023

Nice --- you don't see too many Cody problems involving classes.

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Problem 44262. Multivariate polynomials - overload multiplication

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