# 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 = Y
```

And I got `TypeError: base ring must be an integral domain or a ring of integers mod n`

Your quotient ring

`S`

has divisors of zero, hence the error. In particular, division or fraction field are not well defined for`S`

. And with no division, there is no way to solve matrix equations.