def test_AlternatingGroup():
G = AlternatingGroup(5)
elements = list(G.generate())
assert len(elements) == 60
assert [perm.is_even for perm in elements] == [True] * 60
H = AlternatingGroup(1)
assert H.order() == 1
L = AlternatingGroup(2)
assert L.order() == 1
def test_handle_precomputed_bsgs():
A = AlternatingGroup(5)
A.schreier_sims()
base = A.base
strong_gens = A.strong_gens
result = _handle_precomputed_bsgs(base, strong_gens)
strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
assert strong_gens_distr == result[2]
transversals = result[0]
orbits = result[1]
base_len = len(base)
for i in range(base_len):
for el in orbits[i]:
assert transversals[i][el](base[i]) == el
for j in range(i):
assert transversals[i][el](base[j]) == base[j]
order = 1
for i in range(base_len):
order *= len(orbits[i])
assert A.order() == order
_, transversals = _orbits_transversals_from_bsgs(base, strong_gens_distr)
assert transversals == _handle_precomputed_bsgs(base, strong_gens,
transversals)[0]
assert transversals == _handle_precomputed_bsgs(
base,
strong_gens,
transversals,
basic_orbits=transversals,
strong_gens_distr=strong_gens_distr)[0]
D = DihedralGroup(3)
D.schreier_sims()
assert (_handle_precomputed_bsgs(D.base,
D.strong_gens,
basic_orbits=D.basic_orbits) == ([{
0:
Permutation(2),
1:
Permutation(0, 1, 2),
2:
Permutation(0, 2)
}, {
1:
Permutation(2),
2:
Permutation(1, 2)
}], [[0, 1, 2], [1, 2]], [[
Permutation(0, 1, 2),
Permutation(0, 2),
Permutation(1, 2)
], [Permutation(1, 2)]]))