Get coefficients of symbolic polynomial in Matlab

Question

I have a Matlab function that returns a polynomial of the form:

poly = ax^2 + bx*y + cy^2

where a, b, and c are constants, and x and y are symbolic (class sym).

I want to get the coefficients of the polynomial in the form [a b c], but I'm running into the following problem. If the function returns poly = y^2, then coeffs(poly) = 1. I don't want this – I want it to return [0 0 1].

How can I create a function that will give me the coefficients of a symbolic polynomial in the form that I want?

Answer 1

You can use sym2poly if your polynomial is a function of a single variable like your example y^2:

syms y
p = 2*y^2+3*y+4;
c = sym2poly(p)

which returns

c =

     2     3     4

Use fliplr(c) if you really want the coefficients in the other order. If you're going to be working with polynomials it would probably also be a good idea not to create a variable called poly, which is the name of a function you might want to use.

If you actually need to handle polynomials in multiple variables, you can use MuPAD functions from within Matlab. Here is how you can use MuPAD's coeff to get the coefficients in terms of the order of variable they precede (x or y):

syms x y
p = 2*x^2+3*x*y+4*y;
v = symvar(p);
c = eval(feval(symengine,'coeff',p,v))

If you want to extract all of the information from the polynomial, the poly2list function is quite helpful:

syms x y
p = 2*x^2+3*x*y+4*y;
v = symvar(p);
m = eval(feval(symengine,'poly2list',p,v));
c = m(:,1); % Coefficients
degs = m(:,2:end); % Degree of each variable in each term

The polynomial can then be reconstructed via:

sum(c.*prod(repmat(v,[size(m,1) 1]).^degs,2))

_{By the way, good choice on where you go to school. :-)}

Answer 2

There is also an alternative to this problem. For a given degree, this function returns a polynomial of this degree and its coefficients altogether. Here we go:

 function [polynomial, coefficeint] = makePoly(degree)
 syms x y 
 previous  = 0 ;
 for i=0:degree
     current = expand((x+y)^i);
     previous= current +  previous  ;   
 end
  [~,poly] = coeffs(previous);
 for j= 1:length(poly)
     coefficeint(j) = sym(strcat('a', int2str(j)) );
 end
 polynomial = fliplr(coefficeint)* poly.' ;
 end

Hope this helps.