Checking the cardinality of RLWE rings

check_rlwe_ring_order.sage

# iterate over primes
for i, p in enumerate(Primes()):
    # iterate over cyclotomics
    for n in range(1, i+1):
        # GF(p) is the finite field of order p
        S = PolynomialRing(GF(p), 'x')
        f = cyclotomic_polynomial(n)
        R = QuotientRing(S, f)

        assert R.cardinality() == p ** (f.degree())
        print(f"Checked equality for p == {p}, n == {n}")