Square root of a polynomial over gf

Question

mmavrop 2012-3-27

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Hi all, I would like to ask you, I there is a fanction which calculates the sqaure root of a polynomial over gf..something like this:

    pol=poly2sym(g1.x,'x');
    F = evalin(symengine, 'poly(pol, Dom::GaloisField(2^11))');
    res=feval(symengine, 'sqrt', F)

g1: is the polynomial over gf(2^11)..

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Answer 1

Stefan Wehmeier 2012-3-28

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You will have to do it by hand, that is, use polylib::sqrfree and divide all multiplicities by 2. These multiplicities are in the third, fifth, seventh, ... operand of the factored object, see ?Factored in the MuPAD notebook. Of course, there is no sqrt if one of the multiplicities is odd.

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Answer 2

mmavrop 2012-3-28

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I don't think that I completely understand what I have to do.. I have the polynomial g1 over gf(2^11) so I write in matlab:

pol=poly2sym(g1.x,'x'); 
F = evalin(symengine, 'poly(pol, Dom::GaloisField(2^11))'); 
res=feval(symengine, 'squarefree', F)

and then when you say multiplicities, do you mean the coefficients of "res"? so I have to divide them by 2? When I am writing the above "res" is not a polynomial..

An other question is there a function to inverse a polynomial g1?