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### Finding the kernel of 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.