Matrix derivative validity

def frac_gen(n):
    num = sum(var(f'x0_{i}') * x^(n-1-i) for i in range(n))
    den = sum(var(f'x1_{i}') * x^(n-1-i) for i in range(n))
    expression = num/den
    expression = derivative(expression, x) * den^2
    return expression

def func(n, m):
    for r in range(n-2):
        for c in range(n):
            if r==c:
                m[r,c]=1
            elif r+1==c:
                m[r,c]=-2*x
            elif r+2==c:
                m[r,c]=x^2
    for r in range(-1, -3, -1):
        for c in range(n):
            m[r,c]=var(f'x{2+r}_{c}')
    return m

def matrix_gen(n):
    m = matrix(SR, n, n)
    m = func(n, m)
    return m

# actually check for size n, True means that the conjecture stands
n = 8
print(bool(matrix_gen(n).determinant()==frac_gen(n)))