Python matrix tools over $\mathbb{Z}_q$

Where q is a positive integer greater than 1. All matrix elements are expected to be nonnegative integers in the range [0, q-1]. All computations are carried out modulo q.

The modulus q does not have to be prime for most matrix arithmetical operations (add, multiply), but it must be prime to carry out operations that involve division (invert, solve).

import matrixzq as mzq

mzq.set_modulus(11)
print(f"q={mzq.get_modulus()}")  # 11

# Invert a matrix
M = mzq.new_matrix([[2,3,7],[4,5,10],[9,0,7]])
print("M ="); mzq.print_matrix(M)
IM = mzq.invert(M)
print("IM=invert(M)=");mzq.print_matrix(IM)
# Multiply inverse by itself: should get identity
IMM = mzq.multiply(IM, M)
print(f"IM*M=\n{mzq.sprint_matrix(IMM)}")
I = mzq.identity_matrix(len(M))
print("IM*M==I:", mzq.equality(I, IMM))
assert(mzq.equality(I, IMM))

# Solve the matrix equation Ax = b
A = mzq.new_matrix([[1,1,1,1],[2,4,6,7],[4,5,3,5],[8,9,7,2]])
b = mzq.new_vector([6,0,4,5])
print("A=");mzq.print_matrix(A)
print("b=",end='');mzq.print_vector(b)
x = mzq.solve(A, b)
print("Solve Ax=b => x =", mzq.sprint_vector(x))
# Check result
ax = mzq.multiply(A, x)
print("Check Ax =", mzq.sprint_vector(ax))
print("Ax==b:", mzq.equality(ax, b))
assert(mzq.equality(ax, b))

# Show the transpose of a matrix
print("Transpose A^T=");mzq.print_matrix(mzq.transpose(A))

q=11
M =
[2, 3, 7]
[4, 5, 10]
[9, 0, 7]
IM=invert(M)=
[5, 8, 4]
[1, 4, 9]
[3, 7, 6]
IM*M=
[1, 0, 0]
[0, 1, 0]
[0, 0, 1]
IM*M==I: True
A=
[1, 1, 1, 1]
[2, 4, 6, 7]
[4, 5, 3, 5]
[8, 9, 7, 2]
b=[6, 0, 4, 5]
Solve Ax=b => x = [10, 2, 8, 8]
Check Ax = [6, 0, 4, 5]
Ax==b: True
Transpose A^T=
[1, 2, 4, 8]
[1, 4, 5, 9]
[1, 6, 3, 7]
[1, 7, 5, 2]