83 lines
2.7 KiB
Python
83 lines
2.7 KiB
Python
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"""Test groups defined by the galois module. """
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from sympy.combinatorics.galois import (
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S4TransitiveSubgroups, S5TransitiveSubgroups, S6TransitiveSubgroups,
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find_transitive_subgroups_of_S6,
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)
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from sympy.combinatorics.homomorphisms import is_isomorphic
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from sympy.combinatorics.named_groups import (
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SymmetricGroup, AlternatingGroup, CyclicGroup,
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)
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def test_four_group():
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G = S4TransitiveSubgroups.V.get_perm_group()
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A4 = AlternatingGroup(4)
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assert G.is_subgroup(A4)
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assert G.degree == 4
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assert G.is_transitive()
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assert G.order() == 4
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assert not G.is_cyclic
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def test_M20():
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G = S5TransitiveSubgroups.M20.get_perm_group()
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S5 = SymmetricGroup(5)
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A5 = AlternatingGroup(5)
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assert G.is_subgroup(S5)
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assert not G.is_subgroup(A5)
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assert G.degree == 5
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assert G.is_transitive()
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assert G.order() == 20
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# Setting this True means that for each of the transitive subgroups of S6,
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# we run a test not only on the fixed representation, but also on one freshly
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# generated by the search procedure.
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INCLUDE_SEARCH_REPS = False
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S6_randomized = {}
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if INCLUDE_SEARCH_REPS:
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S6_randomized = find_transitive_subgroups_of_S6(*list(S6TransitiveSubgroups))
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def get_versions_of_S6_subgroup(name):
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vers = [name.get_perm_group()]
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if INCLUDE_SEARCH_REPS:
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vers.append(S6_randomized[name])
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return vers
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def test_S6_transitive_subgroups():
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"""
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Test enough characteristics to distinguish all 16 transitive subgroups.
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"""
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ts = S6TransitiveSubgroups
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A6 = AlternatingGroup(6)
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for name, alt, order, is_isom, not_isom in [
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(ts.C6, False, 6, CyclicGroup(6), None),
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(ts.S3, False, 6, SymmetricGroup(3), None),
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(ts.D6, False, 12, None, None),
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(ts.A4, True, 12, None, None),
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(ts.G18, False, 18, None, None),
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(ts.A4xC2, False, 24, None, SymmetricGroup(4)),
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(ts.S4m, False, 24, SymmetricGroup(4), None),
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(ts.S4p, True, 24, None, None),
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(ts.G36m, False, 36, None, None),
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(ts.G36p, True, 36, None, None),
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(ts.S4xC2, False, 48, None, None),
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(ts.PSL2F5, True, 60, None, None),
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(ts.G72, False, 72, None, None),
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(ts.PGL2F5, False, 120, None, None),
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(ts.A6, True, 360, None, None),
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(ts.S6, False, 720, None, None),
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]:
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for G in get_versions_of_S6_subgroup(name):
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assert G.is_transitive()
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assert G.degree == 6
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assert G.is_subgroup(A6) is alt
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assert G.order() == order
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if is_isom:
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assert is_isomorphic(G, is_isom)
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if not_isom:
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assert not is_isomorphic(G, not_isom)
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