How to get the coefficients of the minimal polynomial ?

Dear All,

I have to find the coefficients of the minimal polynomial of all the matrices stored in a 3-D array. I have tried through the MuPAD but through that I am getting the whole polynomial, If anyone knows the way how to extract only the coefficients from it(i.e. from the polynomial in MuPAD) and then to store them in a vector in matlab, or if any function in Matlab only which can give the coefficients of the minimal polynomial.

Here is the code for the mupad :

nb=mupad;

A:=Dom::Matrix(Dom::Rational)([[1,-1,-1],[1,-2,1],[0,1,-3]]);

delete x: linalg::minpoly(A,x)

This gives the minimal polynomial for the given matrix in 'x'. (I have to do it for the 3-D array of matrices).

If anyone knows some other way too that would be very helpful.

URGENT help needed !!

Thank you, Palash.

Answer 1

[Kai Gehrs]

Hi Palash,

I think the following MATLAB function could do the job for your problem:

function p = minpoly(A)

p = evalin(symengine, ['map(poly2list(linalg::minpoly(' char(sym(A)) ',x)),c->c[1])']);

end

If you add it in MATLAB to your path, then you can call it via:

>> A = [1 -1 -1; 1 -2 1; 0 1 -3]; % minimal polynomial is x^3 + 4*x^2 + x - 1

>> minpoly(A)

ans =

[ 1, 4, 1, -1]

Hope this helps. Inside of MuPAD the function 'poly2list' converts polynomials to a nested list representation containing the information on the coefficients of polynomials.

Best regards,

-- Kai

Answer 2

[Walter Roberson]

Use sym2poly()

Answer 3

[Palash]

Hi Walter,

If I am not wrong then this is the function by which we can get the coefficients for a given polynomial, but not the "minimal polynomial".

I would like to put my questn again : I have to find the coefficients of the minimal polynomial in the Mtalb, or to store the coefficients in a vector in Matlab.

Thanks,

Palash Goyal.

[Walter Roberson]

evalin(symengine) the linalg::minpoly operation, which will return the symbolic result to MATLAB. sym2poly() that result at the MATLAB level.

There is no MATLAB function that does this computation directly.

Answer 4

[Pantelis Sopasakis]

Just my two cents... The code posted by Kai Gehrs will not work if the returned polynomial has some zero coefficients. Try for example the matrix:

A=ones(3,3);

The output will be

[1 -3]

instead of

[1 -3 0]

An m-function that takes care of such a case can be found at https://github.com/alphaville/eat/blob/master/zz_minPolSymb.m