def dup_zz_cyclotomic_poly(n, K):
"""Efficiently generate n-th cyclotomic polnomial. """
h = [K.one, -K.one]
for p, k in factorint(n).items():
h = dup_quo(dup_inflate(h, p, K), h, K)
h = dup_inflate(h, p**(k - 1), K)
return h
def _dup_cyclotomic_decompose(n, K):
H = [[K.one, -K.one]]
for p, k in factorint(n).items():
Q = [dup_quo(dup_inflate(h, p, K), h, K) for h in H]
H.extend(Q)
for i in range(1, k):
Q = [dup_inflate(q, p, K) for q in Q]
H.extend(Q)
return H
def test_dup_inflate():
assert dup_inflate([], 17, ZZ) == []
assert dup_inflate([1, 2, 3], 1, ZZ) == [1, 2, 3]
assert dup_inflate([1, 2, 3], 2, ZZ) == [1, 0, 2, 0, 3]
assert dup_inflate([1, 2, 3], 3, ZZ) == [1, 0, 0, 2, 0, 0, 3]
assert dup_inflate([1, 2, 3], 4, ZZ) == [1, 0, 0, 0, 2, 0, 0, 0, 3]
pytest.raises(IndexError, lambda: dup_inflate([1, 2, 3], 0, ZZ))