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### Finding the kernel of a matrix in a non-integral domain

I have been trying to find the kernel of the matrix in a quotient, for example. If we have the following quotient ring in sage:

R.<t> = PolynomialRing(GF(3),'t') I = R.ideal([t^3]) S = R.quotient_ring(I);

and if I try to find the kernel of the matrix:

E = Matrix(S, ([[0+at+bt^2, 1+at+bt^2, 0+at+bt^2, 0+at+bt^2], [0+at+bt^2, 0+at+bt^2, 0+at+bt^2, 0+at+bt^2], [0+at+bt^2, 0+at+bt^2, 0+at+bt^2, 1+at+bt^2], [0+at+bt^2, 0+at+bt^2, 0+at+bt^2,0+at+bt^2]])) E.kernel()

It gives me the following error: NotImplementedError.

I guess this is because F3[x]/(x^3) is not an integral domain but I would like a way around it.

 2 None tmonteil 20598 ●25 ●146 ●381 http://wiki.sagemath.o...

### Finding the kernel of a matrix in a non-integral domain

I have been trying to find the kernel of the matrix in a quotient, for example. If we have the following quotient ring in sage:

R.<t> = PolynomialRing(GF(3),'t')
I = R.ideal([t^3])
S = R.quotient_ring(I); R.quotient_ring(I);


and if I try to find the kernel of the matrix:

E = Matrix(S, ([[0+at+bt^2, 1+at+bt^2, 0+at+bt^2, 0+at+bt^2],
[0+at+bt^2, 0+at+bt^2, 0+at+bt^2, 0+at+bt^2],
[0+at+bt^2, 0+at+bt^2, 0+at+bt^2, 1+at+bt^2],
[0+at+bt^2, 0+at+bt^2,  0+at+bt^2,0+at+bt^2]]))
E.kernel()([[0+a*t+b*t^2, 1+a*t+b*t^2, 0+a*t+b*t^2, 0+a*t+b*t^2],
[0+a*t+b*t^2, 0+a*t+b*t^2, 0+a*t+b*t^2, 0+a*t+b*t^2],
[0+a*t+b*t^2, 0+a*t+b*t^2, 0+a*t+b*t^2, 1+a*t+b*t^2],
[0+a*t+b*t^2, 0+a*t+b*t^2,  0+a*t+b*t^2,0+a*t+b*t^2]]))
E.kernel()


It gives me the following error: NotImplementedError.

I guess this is because F3[x]/(x^3) is not an integral domain but I would like a way around it.