def dup_zz_cyclotomic_poly(n, K):
"""Efficiently generate n-th cyclotomic polnomial. """
h = [K.one, -K.one]
for p, k in factorint(n).iteritems():
h = dup_quo(dup_inflate(h, p, K), h, K)
h = dup_inflate(h, p**(k - 1), K)
return h
def dup_zz_cyclotomic_poly(n, K):
"""Efficiently generate n-th cyclotomic polnomial. """
h = [K.one,-K.one]
for p, k in factorint(n).iteritems():
h = dup_quo(dup_inflate(h, p, K), h, K)
h = dup_inflate(h, p**(k-1), K)
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]
raises(IndexError, 'dup_inflate([1,2,3], 0, ZZ)')
def _dup_cyclotomic_decompose(n, K):
H = [[K.one, -K.one]]
for p, k in factorint(n).iteritems():
Q = [dup_quo(dup_inflate(h, p, K), h, K) for h in H]
H.extend(Q)
for i in xrange(1, k):
Q = [dup_inflate(q, p, K) for q in Q]
H.extend(Q)
return H
def _dup_cyclotomic_decompose(n, K):
H = [[K.one,-K.one]]
for p, k in factorint(n).iteritems():
Q = [ dup_quo(dup_inflate(h, p, K), h, K) for h in H ]
H.extend(Q)
for i in xrange(1, k):
Q = [ dup_inflate(q, p, K) for q in Q ]
H.extend(Q)
return H
