Find the support of a mpol type variable

Hi,

I have a polynomial of type mpol (ref: GloptiPoly 3: moments, optimization and semidefinite programming (archives-ouvertes.fr)).

It is like a symbolic polynomial defined in MATLAB.

The polynomial is of the form:

f= 1+a1*x1+a2*x2+a3*x3+a4*x4+a5*x1^2+a6*x1*x2+a7*x1*x3+a8*x1*x4+a9*x2^2+a10*x2*x3+......so on

I need to get its support/order of monomial terms, i.e:

[0,0,0,0;

1,0,0,0;

0,1,0,0;

0,0,1,0;

0,0,0,1;

2,0,0,0;

1,1,0,0;

1,0,1,0,

1,0,0,1;

0,2,0,0;

0,1,1,0;

...... so on]

I can get the coeffecients using the coef() function.

But, I need its support/monomial orders.

Is there any matlab function to do so?

Thanks a lot for your help.

Regards

Answer 1

[SAI SRUJAN]

Hi Aksh Chordia,

I understand that you are trying to get the order of monomial terms for a given polynomial.

You can follow the below given example to resolve the issue.

syms a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 x1 x2 x3 x4
f= 1+a1*x1+a2*x2+a3*x3+a4*x4+a5*x1^2+a6*x1*x2+a7*x1*x3+a8*x1*x4+a9*x2^2+a10*x2*x3

f = 

ch=children(f)

ch = 1×11 cell array
    {[a1*x1]}    {[a2*x2]}    {[a3*x3]}    {[a4*x4]}    {[a5*x1^2]}    {[a9*x2^2]}    {[a6*x1*x2]}    {[a7*x1*x3]}    {[a8*x1*x4]}    {[a10*x2*x3]}    {[1]}

order=[];
for i=1:length(ch)
    exp=ch{i};
    coeff=[polynomialDegree(exp,x1)];
    coeff=[coeff polynomialDegree(exp,x2)];
    coeff=[coeff polynomialDegree(exp,x3)];
    coeff=[coeff polynomialDegree(exp,x4)];
    order=[order;coeff];
end
order

order = 11×4

1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 2 0 0 0 0 2 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0

You can use the "children" and "polynomialDegree" MATLAB function to get monomial order of a polynomial.

Degree of polynomial - MATLAB polynomialDegree - MathWorks India

Subexpressions or terms of symbolic expression - MATLAB children - MathWorks India