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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)

n=MS([[17,19],[11,31]])

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

print(M1)

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

print(M2)

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)

n=MS([[17,19],[11,31]])

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

print(M1)

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

print(M2)

[1 1]
[1 1]

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