MatrixSpace quotientRings

asked 2019-05-04 17:42:38 +0200

gelatine1 gravatar image

updated 2019-05-04 17:43:28 +0200

I'm trying to work with a quotingring of a matrix space. Now I use the following code. But since $n$ is my modulus I expect my second matrix to be equal to $M_1$ in this quotient ring. But it's like its just ignoring the fact that its a quotient ring and it does every computation in MS. What am I doing wrong or is my understanding of quotient rings flawed?

Thanks in advance.

MS = MatrixSpace(ZZ,2,2)


R = MS.quotient_ring(MS*n*MS) #or R = MS.quotient_ring(n)
M1 = R([[1,1],[1,1]])


M2 = R(n+M1.lift())


this code gives this as a result

[1 1]
[1 1]

[18 20]
[12 32]
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I think that quotients of matrix rings are not really implemented in Sage in any meaningful way.

John Palmieri gravatar imageJohn Palmieri ( 2019-05-04 23:02:27 +0200 )edit