def test_Module_submodule_from_gens():
T = Poly(cyclotomic_poly(5, x))
A = PowerBasis(T)
gens = [2 * A(0), 2 * A(1), 6 * A(0), 6 * A(1)]
B = A.submodule_from_gens(gens)
# Because the 3rd and 4th generators do not add anything new, we expect
# the cols of the matrix of B to just reproduce the first two gens:
M = gens[0].column().hstack(gens[1].column())
assert B.matrix == M
# At least one generator must be provided:
raises(ValueError, lambda: A.submodule_from_gens([]))
# All generators must belong to A:
raises(ValueError, lambda: A.submodule_from_gens([3 * A(0), B(0)]))
def test_Submodule_add():
T = Poly(cyclotomic_poly(5, x))
A = PowerBasis(T)
B = A.submodule_from_matrix(DomainMatrix([
[4, 0, 0, 0],
[0, 4, 0, 0],
], (2, 4), ZZ).transpose(),
denom=6)
C = A.submodule_from_matrix(DomainMatrix([
[0, 10, 0, 0],
[0, 0, 7, 0],
], (2, 4), ZZ).transpose(),
denom=15)
D = A.submodule_from_matrix(DomainMatrix([
[20, 0, 0, 0],
[0, 20, 0, 0],
[0, 0, 14, 0],
], (3, 4), ZZ).transpose(),
denom=30)
assert B + C == D
U = Poly(cyclotomic_poly(7, x))
Z = PowerBasis(U)
Y = Z.submodule_from_gens([Z(0), Z(1)])
raises(TypeError, lambda: B + Y)
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)
