Problem 44263. Multivariate polynomials - emulate symbolic form

Created by Andrew Newell

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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.

In <https://www.mathworks.com/matlabcentral/cody/problems/44262-multivariate-polynomials-overload-multiplication Problem 44262> I asked you to create a class |mPoly| with overloaded multiplication, so a product of two polynomials can be expressed in the form |p = p1*p2|. However, the method of constructing these polynomials is still somewhat unintuitive. In the <https://www.mathworks.com/products/symbolic.html Symbolic Math Toolbox>, one can simply define some variables,

syms x y z

and then create a polynomial:

p = 2*x*y + 3*x^5*z;

x = mPolySym('x')

x =

mPolySym with properties:

varnames: "x"
       exponents: 1
    coefficients: 1

r = mPolySym(pi)

r =

mPolySym with properties:

varnames: [0×0 string]
       exponents: 1
    coefficients: 3.1416

Also modify the method |mtimes| 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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