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from sympy.combinatorics.permutations import Permutation |
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from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup, DihedralGroup |
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from sympy.matrices import Matrix |
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def test_pc_presentation(): |
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Groups = [SymmetricGroup(3), SymmetricGroup(4), SymmetricGroup(9).sylow_subgroup(3), |
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SymmetricGroup(9).sylow_subgroup(2), SymmetricGroup(8).sylow_subgroup(2), DihedralGroup(10)] |
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S = SymmetricGroup(125).sylow_subgroup(5) |
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G = S.derived_series()[2] |
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Groups.append(G) |
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G = SymmetricGroup(25).sylow_subgroup(5) |
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Groups.append(G) |
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S = SymmetricGroup(11**2).sylow_subgroup(11) |
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G = S.derived_series()[2] |
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Groups.append(G) |
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for G in Groups: |
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PcGroup = G.polycyclic_group() |
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collector = PcGroup.collector |
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pc_presentation = collector.pc_presentation |
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pcgs = PcGroup.pcgs |
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free_group = collector.free_group |
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free_to_perm = {} |
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for s, g in zip(free_group.symbols, pcgs): |
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free_to_perm[s] = g |
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for k, v in pc_presentation.items(): |
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k_array = k.array_form |
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if v != (): |
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v_array = v.array_form |
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lhs = Permutation() |
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for gen in k_array: |
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s = gen[0] |
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e = gen[1] |
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lhs = lhs*free_to_perm[s]**e |
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if v == (): |
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assert lhs.is_identity |
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continue |
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rhs = Permutation() |
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for gen in v_array: |
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s = gen[0] |
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e = gen[1] |
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rhs = rhs*free_to_perm[s]**e |
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assert lhs == rhs |
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def test_exponent_vector(): |
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Groups = [SymmetricGroup(3), SymmetricGroup(4), SymmetricGroup(9).sylow_subgroup(3), |
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SymmetricGroup(9).sylow_subgroup(2), SymmetricGroup(8).sylow_subgroup(2)] |
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for G in Groups: |
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PcGroup = G.polycyclic_group() |
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collector = PcGroup.collector |
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pcgs = PcGroup.pcgs |
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for gen in G.generators: |
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exp = collector.exponent_vector(gen) |
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g = Permutation() |
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for i in range(len(exp)): |
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g = g*pcgs[i]**exp[i] if exp[i] else g |
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assert g == gen |
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def test_induced_pcgs(): |
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G = [SymmetricGroup(9).sylow_subgroup(3), SymmetricGroup(20).sylow_subgroup(2), AlternatingGroup(4), |
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DihedralGroup(4), DihedralGroup(10), DihedralGroup(9), SymmetricGroup(3), SymmetricGroup(4)] |
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for g in G: |
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PcGroup = g.polycyclic_group() |
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collector = PcGroup.collector |
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gens = list(g.generators) |
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ipcgs = collector.induced_pcgs(gens) |
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m = [] |
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for i in ipcgs: |
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m.append(collector.exponent_vector(i)) |
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assert Matrix(m).is_upper |
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