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from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup,\ |
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CyclicGroup |
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from sympy.combinatorics.testutil import _verify_bsgs, _cmp_perm_lists,\ |
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_naive_list_centralizer, _verify_centralizer,\ |
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_verify_normal_closure |
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from sympy.combinatorics.permutations import Permutation |
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from sympy.combinatorics.perm_groups import PermutationGroup |
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from sympy.core.random import shuffle |
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def test_cmp_perm_lists(): |
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S = SymmetricGroup(4) |
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els = list(S.generate_dimino()) |
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other = els.copy() |
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shuffle(other) |
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assert _cmp_perm_lists(els, other) is True |
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def test_naive_list_centralizer(): |
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S = SymmetricGroup(3) |
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A = AlternatingGroup(3) |
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assert _naive_list_centralizer(S, S) == [Permutation([0, 1, 2])] |
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assert PermutationGroup(_naive_list_centralizer(S, A)).is_subgroup(A) |
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def test_verify_bsgs(): |
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S = SymmetricGroup(5) |
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S.schreier_sims() |
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base = S.base |
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strong_gens = S.strong_gens |
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assert _verify_bsgs(S, base, strong_gens) is True |
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assert _verify_bsgs(S, base[:-1], strong_gens) is False |
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assert _verify_bsgs(S, base, S.generators) is False |
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def test_verify_centralizer(): |
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S = SymmetricGroup(3) |
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A = AlternatingGroup(3) |
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triv = PermutationGroup([Permutation([0, 1, 2])]) |
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assert _verify_centralizer(S, S, centr=triv) |
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assert _verify_centralizer(S, A, centr=A) |
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def test_verify_normal_closure(): |
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S = SymmetricGroup(3) |
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A = AlternatingGroup(3) |
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assert _verify_normal_closure(S, A, closure=A) |
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S = SymmetricGroup(5) |
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A = AlternatingGroup(5) |
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C = CyclicGroup(5) |
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assert _verify_normal_closure(S, A, closure=A) |
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assert _verify_normal_closure(S, C, closure=A) |
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