56 lines
1.7 KiB
Python
56 lines
1.7 KiB
Python
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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[:]
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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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# verified by GAP
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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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# verified by GAP
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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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# verified by GAP
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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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