GF multiply by constant to matrix multiplication

gf_mul_linear.sage

x = polygen(GF(2))
mod = x.parent().irreducible_element(8, algorithm='random')
F = GF(2^8, 'a', modulus=mod)

def get_multiply_matrix(mul, mod):
	return mul.polynomial()(matrix.companion(mod))

mul = F.random_element()
T = get_multiply_matrix(mul, mod)
for _ in range(100):
	r = F.random_element()
	va = vector(r.polynomial().padded_list(8))
	vb = vector((r * mul).polynomial().padded_list(8))
	assert T * va == vb