def test_Module_zero():
T = Poly(cyclotomic_poly(5, x))
A = PowerBasis(T)
B = A.submodule_from_matrix(2 * DomainMatrix.eye(4, ZZ))
assert A.zero().col.flat() == [0, 0, 0, 0]
assert A.zero().module == A
assert B.zero().col.flat() == [0, 0, 0, 0]
assert B.zero().module == B
def test_ModuleElement_mod():
T = Poly(cyclotomic_poly(5, x))
A = PowerBasis(T)
e = A(to_col([1, 15, 8, 0]), denom=2)
assert e % 7 == A(to_col([1, 1, 8, 0]), denom=2)
assert e % QQ(1, 2) == A.zero()
assert e % QQ(1, 3) == A(to_col([1, 1, 0, 0]), denom=6)
B = A.submodule_from_gens([A(0), 5 * A(1), 3 * A(2), A(3)])
assert e % B == A(to_col([1, 5, 2, 0]), denom=2)
C = B.whole_submodule()
raises(TypeError, lambda: e % C)
