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