ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 28 May 2018 03:43:10 +0200kernel of a matrix defined over polynomial ringshttps://ask.sagemath.org/question/42453/kernel-of-a-matrix-defined-over-polynomial-rings/ 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?Mon, 28 May 2018 00:40:42 +0200https://ask.sagemath.org/question/42453/kernel-of-a-matrix-defined-over-polynomial-rings/Answer by nbruin for <p>I have a matrix defined as a function of variables in a polynomial ring defined over finite field as follows-</p>
<pre><code> Gr.<xp,yp>=LaurentPolynomialRing(GF(2));
M=Matrix(Gr,[[xp-1,0],
[yp-1,0],
[0,(yp^(-1))-1],
[0,-(xp^(-1))+1]]);
</code></pre>
<p>I want to calculate the kernel of this matrix but the kernel function </p>
<pre><code>M.kernel()
</code></pre>
<p>gives an error. What am I doing wrong?</p>
https://ask.sagemath.org/question/42453/kernel-of-a-matrix-defined-over-polynomial-rings/?answer=42454#post-id-42454You'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.Mon, 28 May 2018 03:43:10 +0200https://ask.sagemath.org/question/42453/kernel-of-a-matrix-defined-over-polynomial-rings/?answer=42454#post-id-42454