121 lines
4.4 KiB
Python
121 lines
4.4 KiB
Python
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from sympy.combinatorics.named_groups import SymmetricGroup, DihedralGroup,\
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AlternatingGroup
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from sympy.combinatorics.permutations import Permutation
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from sympy.combinatorics.util import _check_cycles_alt_sym, _strip,\
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_distribute_gens_by_base, _strong_gens_from_distr,\
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_orbits_transversals_from_bsgs, _handle_precomputed_bsgs, _base_ordering,\
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_remove_gens
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from sympy.combinatorics.testutil import _verify_bsgs
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def test_check_cycles_alt_sym():
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perm1 = Permutation([[0, 1, 2, 3, 4, 5, 6], [7], [8], [9]])
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perm2 = Permutation([[0, 1, 2, 3, 4, 5], [6, 7, 8, 9]])
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perm3 = Permutation([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]])
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assert _check_cycles_alt_sym(perm1) is True
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assert _check_cycles_alt_sym(perm2) is False
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assert _check_cycles_alt_sym(perm3) is False
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def test_strip():
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D = DihedralGroup(5)
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D.schreier_sims()
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member = Permutation([4, 0, 1, 2, 3])
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not_member1 = Permutation([0, 1, 4, 3, 2])
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not_member2 = Permutation([3, 1, 4, 2, 0])
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identity = Permutation([0, 1, 2, 3, 4])
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res1 = _strip(member, D.base, D.basic_orbits, D.basic_transversals)
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res2 = _strip(not_member1, D.base, D.basic_orbits, D.basic_transversals)
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res3 = _strip(not_member2, D.base, D.basic_orbits, D.basic_transversals)
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assert res1[0] == identity
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assert res1[1] == len(D.base) + 1
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assert res2[0] == not_member1
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assert res2[1] == len(D.base) + 1
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assert res3[0] != identity
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assert res3[1] == 2
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def test_distribute_gens_by_base():
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base = [0, 1, 2]
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gens = [Permutation([0, 1, 2, 3]), Permutation([0, 1, 3, 2]),
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Permutation([0, 2, 3, 1]), Permutation([3, 2, 1, 0])]
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assert _distribute_gens_by_base(base, gens) == [gens,
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[Permutation([0, 1, 2, 3]),
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Permutation([0, 1, 3, 2]),
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Permutation([0, 2, 3, 1])],
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[Permutation([0, 1, 2, 3]),
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Permutation([0, 1, 3, 2])]]
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def test_strong_gens_from_distr():
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strong_gens_distr = [[Permutation([0, 2, 1]), Permutation([1, 2, 0]),
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Permutation([1, 0, 2])], [Permutation([0, 2, 1])]]
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assert _strong_gens_from_distr(strong_gens_distr) == \
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[Permutation([0, 2, 1]),
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Permutation([1, 2, 0]),
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Permutation([1, 0, 2])]
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def test_orbits_transversals_from_bsgs():
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S = SymmetricGroup(4)
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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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strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
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result = _orbits_transversals_from_bsgs(base, strong_gens_distr)
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orbits = result[0]
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transversals = result[1]
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base_len = len(base)
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for i in range(base_len):
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for el in orbits[i]:
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assert transversals[i][el](base[i]) == el
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for j in range(i):
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assert transversals[i][el](base[j]) == base[j]
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order = 1
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for i in range(base_len):
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order *= len(orbits[i])
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assert S.order() == order
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def test_handle_precomputed_bsgs():
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A = AlternatingGroup(5)
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A.schreier_sims()
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base = A.base
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strong_gens = A.strong_gens
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result = _handle_precomputed_bsgs(base, strong_gens)
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strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
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assert strong_gens_distr == result[2]
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transversals = result[0]
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orbits = result[1]
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base_len = len(base)
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for i in range(base_len):
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for el in orbits[i]:
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assert transversals[i][el](base[i]) == el
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for j in range(i):
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assert transversals[i][el](base[j]) == base[j]
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order = 1
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for i in range(base_len):
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order *= len(orbits[i])
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assert A.order() == order
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def test_base_ordering():
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base = [2, 4, 5]
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degree = 7
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assert _base_ordering(base, degree) == [3, 4, 0, 5, 1, 2, 6]
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def test_remove_gens():
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S = SymmetricGroup(10)
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base, strong_gens = S.schreier_sims_incremental()
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new_gens = _remove_gens(base, strong_gens)
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assert _verify_bsgs(S, base, new_gens) is True
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A = AlternatingGroup(7)
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base, strong_gens = A.schreier_sims_incremental()
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new_gens = _remove_gens(base, strong_gens)
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assert _verify_bsgs(A, base, new_gens) is True
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D = DihedralGroup(2)
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base, strong_gens = D.schreier_sims_incremental()
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new_gens = _remove_gens(base, strong_gens)
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assert _verify_bsgs(D, base, new_gens) is True
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