def test_induced_pcgs():
G = SymmetricGroup(9).sylow_subgroup(3)
PcGroup = G.polycyclic_group()
collector = PcGroup.collector
gens = [G[0], G[1]]
ipcgs = collector.induced_pcgs(gens)
order = [gen.order() for gen in ipcgs]
assert order == [3, 3]
G = SymmetricGroup(20).sylow_subgroup(2)
PcGroup = G.polycyclic_group()
collector = PcGroup.collector
gens = [G[0], G[1], G[2], G[3]]
ipcgs = collector.induced_pcgs(gens)
order = [gen.order() for gen in ipcgs]
assert order == [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
def test_pc_presentation():
Groups = [
SymmetricGroup(3),
SymmetricGroup(4),
SymmetricGroup(9).sylow_subgroup(3),
SymmetricGroup(9).sylow_subgroup(2),
SymmetricGroup(8).sylow_subgroup(2)
]
S = SymmetricGroup(125).sylow_subgroup(5)
G = S.derived_series()[2]
Groups.append(G)
G = SymmetricGroup(25).sylow_subgroup(5)
Groups.append(G)
S = SymmetricGroup(11**2).sylow_subgroup(11)
G = S.derived_series()[2]
Groups.append(G)
for G in Groups:
PcGroup = G.polycyclic_group()
collector = PcGroup.collector
pc_presentation = collector.pc_presentation
pcgs = PcGroup.pcgs
free_group = collector.free_group
free_to_perm = {}
for s, g in zip(free_group.symbols, pcgs):
free_to_perm[s] = g
for k, v in pc_presentation.items():
k_array = k.array_form
if v != ():
v_array = v.array_form
lhs = Permutation()
for gen in k_array:
s = gen[0]
e = gen[1]
lhs = lhs * free_to_perm[s]**e
if v == ():
assert lhs.is_identity
continue
rhs = Permutation()
for gen in v_array:
s = gen[0]
e = gen[1]
rhs = rhs * free_to_perm[s]**e
assert lhs == rhs
