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)]]))
def test_strip():
D = DihedralGroup(5)
D.schreier_sims()
member = Permutation([4, 0, 1, 2, 3])
not_member1 = Permutation([0, 1, 4, 3, 2])
not_member2 = Permutation([3, 1, 4, 2, 0])
identity = Permutation([0, 1, 2, 3, 4])
res1 = _strip(member, D.base, D.basic_orbits, D.basic_transversals)
res2 = _strip(not_member1, D.base, D.basic_orbits, D.basic_transversals)
res3 = _strip(not_member2, D.base, D.basic_orbits, D.basic_transversals)
assert res1[0] == identity
assert res1[1] == len(D.base) + 1
assert res2[0] == not_member1
assert res2[1] == len(D.base) + 1
assert res3[0] != identity
assert res3[1] == 2
