how to find irreducible factors of a polynomial

i have a polynomial p in binary format and i want to get all the irreducible factors of this polynomial.

p = [ 1 1 1 1 0 1 0 1 1 0 0 1];

thanks

monica

Answer 1

[Roger Stafford]

What ring or field can the coefficients of your reduced polynomials belong to? It makes a difference as to their classification as irreducible. For one field they are and another they aren't.

If the field is simply all reals, then you can use 'roots' to determine the irreducible factors. A pair of conjugate roots will together constitute a quadratic irreducible factor while real roots will give you simple first degree factors.

Answer 2

[Walter Roberson]

R = feval(symengine, 'Dom::IntegerMod', 2);   %ring over binary
ps = poly2sym(p);                             %convert to symbolic poly
ppoly = feval(symengine, 'poly', ps, R);      %convert symbolic poly to polynomial over ring
pfact = factor(ppoly, x);                     %factor it into irreducible terms
numfact = length(pfact);
facts = sym(zeros(1,numfact));
for idx = 1 : numfact
   facts(idx) = feval(symengine, 'expr', pfact(idx));   %convert them to polynomials
end

Note: this happens to return the constant polynomial 1 as one of the factors.

There might be an easier way using http://www.mathworks.com/matlabcentral/fileexchange/32872-a-toolbox-for-simple-finite-field-operation