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kernel of a matrix defined over polynomial rings

asked 2018-05-27 17:40:42 -0500

arpit gravatar image

I have a matrix defined as a function of variables in a polynomial ring defined over finite field as follows-

              Gr.<xp,yp>=LaurentPolynomialRing(GF(2));
              M=Matrix(Gr,[[xp-1,0],
                                 [yp-1,0],
                                 [0,(yp^(-1))-1],
                                 [0,-(xp^(-1))+1]]);

I want to calculate the kernel of this matrix but the kernel function

M.kernel()

gives an error. What am I doing wrong?

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answered 2018-05-27 20:43:10 -0500

nbruin gravatar image

You're not doing something wrong. You are just asking something that hasn't been implemented. As a workaround you can look at the kernel over the fraction field:

M.change_ring(Gr.fraction_field()).kernel()

From that you may be able to glean enough information on the kernel over your laurent polynomial ring. In general, modules over polynomial rings can get pretty involved.

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Asked: 2018-05-27 17:40:42 -0500

Seen: 28 times

Last updated: May 27