Solve Matrix Multiplication Equation on Quotient Polynomial Ring
How to solve matrix multiplication equation on quotient polynomial ring? my try:
## polynomial ring
K = 4
L = 4
N = 256
F = GF(8380417)
R = F['x']
S = R.quotient(x^N+1, 'x')
A = random_matrix(S, K, L, distribution='gen')
s1_coef = [ [randint(0, 2) for i in range(N+1)] for _ in range(L)]
s1 = vector([S(_) for _ in s1_coef])
t = A*s1
A.solve_right(t) # get X for AX = YAnd I got TypeError: base ring must be an integral domain or a ring of integers mod n
Your quotient ring
Shas divisors of zero, hence the error. In particular, division or fraction field are not well defined forS. And with no division, there is no way to solve matrix equations.