Problem 44263. Multivariate polynomials - emulate symbolic form

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>In</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication\"><w:r><w:t>Problem 44262</w:t></w:r></w:hyperlink><w:r><w:t> I asked you to create a class</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>mPoly</w:t></w:r><w:r><w:t> with overloaded multiplication, so a product of two polynomials can be expressed in the form</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>p = p1*p2</w:t></w:r><w:r><w:t>. However, the method of constructing these polynomials is still somewhat unintuitive. In the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/products/symbolic.html\"><w:r><w:t>Symbolic Math Toolbox</w:t></w:r></w:hyperlink><w:r><w:t>, one can simply define some variables,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[syms x y z]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>and then create a polynomial:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[p = 2*x*y + 3*x^5*z;]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>We would like to do something like that here. As a start, create a class</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>mPolySym</w:t></w:r><w:r><w:t> with 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</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>varnames</w:t></w:r><w:r><w:t>, where the first two properties are the same as in previous problems 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>varnames</w:t></w:r><w:r><w:t> is a</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/help/matlab/characters-and-strings.html\"><w:r><w:t>string array</w:t></w:r></w:hyperlink><w:r><w:t>. The constructor should accept a numeric, char or string input, e.g.,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[x = mPolySym('x')\n\nx = \n\nmPolySym with properties:\n\n varnames: \"x\"\n exponents: 1\n coefficients: 1\n\nr = mPolySym(pi)\n\nr = \n\nmPolySym with properties:\n\n varnames: [0×0 string]\n exponents: 1\n coefficients: 3.1416]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Also modify the method</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>mtimes</w:t></w:r><w:r><w:t> from the previous problem so it can multiply polynomials with different variable names.</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>"}]}

In <a href = "https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication">Problem 44262</a> I asked you to create a class <tt>mPoly</tt> with overloaded multiplication, so a product of two polynomials can be expressed in the form <tt>p = p1*p2</tt>. However, the method of constructing these polynomials is still somewhat unintuitive. In the <a href = "https://www.mathworks.com/products/symbolic.html">Symbolic Math Toolbox</a>, one can simply define some variables,<pre class="language-matlab">syms x y z
</pre>and then create a polynomial:<pre class="language-matlab">p = 2*x*y + 3*x^5*z;
</pre>We would like to do something like that here. As a start, create a class <tt>mPolySym</tt> with properties <tt>exponents</tt> and <tt>coefficients</tt>, and <tt>varnames</tt>, where the first two properties are the same as in previous problems and <tt>varnames</tt> is a <a href = "https://www.mathworks.com/help/matlab/characters-and-strings.html">string array</a>. The constructor should accept a numeric, char or string input, e.g.,<pre class="language-matlab">x = mPolySym('x')
</pre><pre class="language-matlab">x = 
</pre><pre class="language-matlab">mPolySym with properties:
</pre><pre> varnames: "x"
 exponents: 1
 coefficients: 1</pre><pre class="language-matlab">r = mPolySym(pi)
</pre><pre class="language-matlab">r = 
</pre><pre class="language-matlab">mPolySym with properties:
</pre><pre> varnames: [0×0 string]
 exponents: 1
 coefficients: 3.1416</pre>Also modify the method <tt>mtimes</tt> from the previous problem so it can multiply polynomials with different variable names.

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Problem 44263. Multivariate polynomials - emulate symbolic form

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