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