def dup_cyclotomic_p(f, K, irreducible=False):
"""
Efficiently test if ``f`` is a cyclotomic polnomial.
Examples
========
>>> from sympy.polys.factortools import dup_cyclotomic_p
>>> from sympy.polys.domains import ZZ
>>> f = [1, 0, 1, 0, 0, 0,-1, 0, 1, 0,-1, 0, 0, 0, 1, 0, 1]
>>> dup_cyclotomic_p(f, ZZ)
False
>>> g = [1, 0, 1, 0, 0, 0,-1, 0,-1, 0,-1, 0, 0, 0, 1, 0, 1]
>>> dup_cyclotomic_p(g, ZZ)
True
"""
if K.is_QQ:
try:
K0, K = K, K.get_ring()
f = dup_convert(f, K0, K)
except CoercionFailed:
return False
elif not K.is_ZZ:
return False
lc = dup_LC(f, K)
tc = dup_TC(f, K)
if lc != 1 or (tc != -1 and tc != 1):
return False
if not irreducible:
coeff, factors = dup_factor_list(f, K)
if coeff != K.one or factors != [(f, 1)]:
return False
n = dup_degree(f)
g, h = [], []
for i in xrange(n, -1, -2):
g.insert(0, f[i])
for i in xrange(n - 1, -1, -2):
h.insert(0, f[i])
g = dup_sqr(dup_strip(g), K)
h = dup_sqr(dup_strip(h), K)
F = dup_sub(g, dup_lshift(h, 1, K), K)
if K.is_negative(dup_LC(F, K)):
F = dup_neg(F, K)
if F == f:
return True
g = dup_mirror(f, K)
if K.is_negative(dup_LC(g, K)):
g = dup_neg(g, K)
if F == g and dup_cyclotomic_p(g, K):
return True
G = dup_sqf_part(F, K)
if dup_sqr(G, K) == F and dup_cyclotomic_p(G, K):
return True
return False
def dup_zz_cyclotomic_p(f, K, irreducible=False):
"""
Efficiently test if ``f`` is a cyclotomic polnomial.
**Examples**
>>> from sympy.polys.factortools import dup_zz_cyclotomic_p
>>> from sympy.polys.domains import ZZ
>>> f = [1, 0, 1, 0, 0, 0,-1, 0, 1, 0,-1, 0, 0, 0, 1, 0, 1]
>>> dup_zz_cyclotomic_p(f, ZZ)
False
>>> g = [1, 0, 1, 0, 0, 0,-1, 0,-1, 0,-1, 0, 0, 0, 1, 0, 1]
>>> dup_zz_cyclotomic_p(g, ZZ)
True
"""
if K.is_QQ:
try:
K0, K = K, K.get_ring()
f = dup_convert(f, K0, K)
except CoercionFailed:
return False
elif not K.is_ZZ:
return False
lc = dup_LC(f, K)
tc = dup_TC(f, K)
if lc != 1 or (tc != -1 and tc != 1):
return False
if not irreducible:
coeff, factors = dup_factor_list(f, K)
if coeff != K.one or factors != [(f, 1)]:
return False
n = dup_degree(f)
g, h = [], []
for i in xrange(n, -1, -2):
g.insert(0, f[i])
for i in xrange(n-1, -1, -2):
h.insert(0, f[i])
g = dup_sqr(dup_strip(g), K)
h = dup_sqr(dup_strip(h), K)
F = dup_sub(g, dup_lshift(h, 1, K), K)
if K.is_negative(dup_LC(F, K)):
F = dup_neg(F, K)
if F == f:
return True
g = dup_mirror(f, K)
if K.is_negative(dup_LC(g, K)):
g = dup_neg(g, K)
if F == g and dup_zz_cyclotomic_p(g, K):
return True
G = dup_sqf_part(F, K)
if dup_sqr(G, K) == F and dup_zz_cyclotomic_p(G, K):
return True
return False
def test_dup_mirror():
assert dup_mirror([], ZZ) == []
assert dup_mirror([1], ZZ) == [1]
assert dup_mirror([1, 2, 3, 4, 5], ZZ) == [1, -2, 3, -4, 5]
assert dup_mirror([1, 2, 3, 4, 5, 6], ZZ) == [-1, 2, -3, 4, -5, 6]
def test_dup_mirror():
assert dup_mirror([], ZZ) == []
assert dup_mirror([1], ZZ) == [1]
assert dup_mirror([1, 2, 3, 4, 5], ZZ) == [1, -2, 3, -4, 5]
assert dup_mirror([1, 2, 3, 4, 5, 6], ZZ) == [-1, 2, -3, 4, -5, 6]
