def test_SymmetricGroup():
G = SymmetricGroup(5)
elements = list(G.generate())
assert (G.generators[0]).size == 5
assert len(elements) == 120
assert G.is_solvable is False
assert G.is_abelian is False
assert G.is_nilpotent is False
assert G.is_transitive() is True
H = SymmetricGroup(1)
assert H.order() == 1
L = SymmetricGroup(2)
assert L.order() == 2
def test_SymmetricGroup():
G = SymmetricGroup(5)
elements = list(G.generate())
assert (G.generators[0]).size == 5
assert len(elements) == 120
assert G.is_solvable is False
assert G.is_abelian is False
assert G.is_nilpotent is False
assert G.is_transitive() is True
H = SymmetricGroup(1)
assert H.order() == 1
L = SymmetricGroup(2)
assert L.order() == 2
def test_orbits_transversals_from_bsgs():
S = SymmetricGroup(4)
S.schreier_sims()
base = S.base
strong_gens = S.strong_gens
strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
result = _orbits_transversals_from_bsgs(base, strong_gens_distr)
orbits = result[0]
transversals = 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 S.order() == order
def test_orbits_transversals_from_bsgs():
S = SymmetricGroup(4)
S.schreier_sims()
base = S.base
strong_gens = S.strong_gens
strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
result = _orbits_transversals_from_bsgs(base, strong_gens_distr)
orbits = result[0]
transversals = 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 S.order() == order