def test_Domain_cyclotomic_field():
K = ZZ.cyclotomic_field(12)
assert K.ext.minpoly == Poly(cyclotomic_poly(12))
assert K.dom == QQ
F = QQ.cyclotomic_field(3)
assert F.ext.minpoly == Poly(cyclotomic_poly(3))
assert F.dom == QQ
E = F.cyclotomic_field(4)
assert field_isomorphism(E.ext, K.ext) is not None
assert E.dom == QQ
def test_PowerBasis_element__conversions():
k = QQ.cyclotomic_field(5)
L = QQ.cyclotomic_field(7)
B = PowerBasis(k)
# ANP --> PowerBasisElement
a = k([QQ(1, 2), QQ(1, 3), 5, 7])
e = B.element_from_ANP(a)
assert e.coeffs == [42, 30, 2, 3]
assert e.denom == 6
# PowerBasisElement --> ANP
assert e.to_ANP() == a
# Cannot convert ANP from different field
d = L([QQ(1, 2), QQ(1, 3), 5, 7])
raises(UnificationFailed, lambda: B.element_from_ANP(d))
# AlgebraicNumber --> PowerBasisElement
alpha = k.to_alg_num(a)
eps = B.element_from_alg_num(alpha)
assert eps.coeffs == [42, 30, 2, 3]
assert eps.denom == 6
# PowerBasisElement --> AlgebraicNumber
assert eps.to_alg_num() == alpha
# Cannot convert AlgebraicNumber from different field
delta = L.to_alg_num(d)
raises(UnificationFailed, lambda: B.element_from_alg_num(delta))
# When we don't know the field:
C = PowerBasis(k.ext.minpoly)
# Can convert from AlgebraicNumber:
eps = C.element_from_alg_num(alpha)
assert eps.coeffs == [42, 30, 2, 3]
assert eps.denom == 6
# But can't convert back:
raises(StructureError, lambda: eps.to_alg_num())