def test_orbits(): a = Permutation([2, 0, 1]) b = Permutation([2, 1, 0]) g = PermutationGroup([a, b]) assert g.orbit(0) == {0, 1, 2} assert g.orbits() == [{0, 1, 2}] assert g.is_transitive() and g.is_transitive(strict=False) assert g.orbit_transversal(0) == \ [Permutation( [0, 1, 2]), Permutation([2, 0, 1]), Permutation([1, 2, 0])] assert g.orbit_transversal(0, True) == \ [(0, Permutation([0, 1, 2])), (2, Permutation([2, 0, 1])), (1, Permutation([1, 2, 0]))] G = DihedralGroup(6) transversal, slps = _orbit_transversal(G.degree, G.generators, 0, True, slp=True) for i, t in transversal: slp = slps[i] w = G.identity for s in slp: w = G.generators[s]*w assert w == t a = Permutation(list(range(1, 100)) + [0]) G = PermutationGroup([a]) assert [min(o) for o in G.orbits()] == [0] G = PermutationGroup(rubik_cube_generators()) assert [min(o) for o in G.orbits()] == [0, 1] assert not G.is_transitive() and not G.is_transitive(strict=False) G = PermutationGroup([Permutation(0, 1, 3), Permutation(3)(0, 1)]) assert not G.is_transitive() and G.is_transitive(strict=False) assert PermutationGroup( Permutation(3)).is_transitive(strict=False) is False
def test_rubik(): skip('takes too much time') G = PermutationGroup(rubik_cube_generators()) assert G.order() == 43252003274489856000 G1 = PermutationGroup(G[:3]) assert G1.order() == 170659735142400 assert not G1.is_normal(G) G2 = G.normal_closure(G1.generators) assert G2.is_subgroup(G)
def test_rubik1(): gens = rubik_cube_generators() gens1 = [gens[0]] + [p**2 for p in gens[1:]] G1 = PermutationGroup(gens1) assert G1.order() == 19508428800 gens2 = [p**2 for p in gens] G2 = PermutationGroup(gens2) assert G2.order() == 663552 assert G2.is_subgroup(G1) C1 = G1.commutator() assert C1.order() == 4877107200 assert C1.is_subgroup(G1) assert not G2.is_subgroup(C1)
def test_rubik1(): gens = rubik_cube_generators() gens1 = [gens[0]] + [p**2 for p in gens[1:]] G1 = PermutationGroup(gens1) assert G1.order() == 19508428800 gens2 = [p**2 for p in gens] G2 = PermutationGroup(gens2) assert G2.order() == 663552 assert G2.is_subgroup(G1) C1 = G1.derived_subgroup() assert C1.order() == 4877107200 assert C1.is_subgroup(G1) assert not G2.is_subgroup(C1)
def test_rubik1(): gens = rubik_cube_generators() gens1 = [gens[-1]] + [p**2 for p in gens[1:]] G1 = PermutationGroup(gens1) assert G1.order() == 19508428800 gens2 = [p**2 for p in gens] G2 = PermutationGroup(gens2) assert G2.order() == 663552 assert G2.is_subgroup(G1, 0) C1 = G1.derived_subgroup() assert C1.order() == 4877107200 assert C1.is_subgroup(G1, 0) assert not G2.is_subgroup(C1, 0) G = RubikGroup(2) assert G.order() == 3674160
def test_orbits(): a = Permutation([2, 0, 1]) b = Permutation([2, 1, 0]) g = PermutationGroup([a, b]) assert g.orbit(0) == set([0, 1, 2]) assert g.orbits() == [set([0, 1, 2])] assert g.is_transitive() assert g.orbits(rep=True) == [0] assert g.orbit_traversal(0) == \ [Permutation([0,1,2]), Permutation([1,2,0]), Permutation([2,0,1])] orbt = g.orbit_traversal(1, af=True) assert g.orbit_traversal(1, af=True) == [[2, 0, 1], [0, 1, 2], [1, 2, 0]] a = Permutation(range(1, 100) + [0]) G = PermutationGroup([a]) assert G.orbits(rep=True) == [0] gens = rubik_cube_generators() g = PermutationGroup(gens, 48) assert g.orbits(rep=True) == [0, 1] assert not g.is_transitive()
def test_orbits(): a = Permutation([2, 0, 1]) b = Permutation([2, 1, 0]) g = PermutationGroup([a, b]) assert g.orbit(0) == set([0, 1, 2]) assert g.orbits() == [set([0, 1, 2])] assert g.is_transitive() and g.is_transitive(strict=False) assert g.orbit_transversal(0) == \ [Permutation([0, 1, 2]), Permutation([2, 0, 1]), Permutation([1, 2, 0])] assert g.orbit_transversal(0, True) == \ [(0, Permutation([0, 1, 2])), (2, Permutation([2, 0, 1])), \ (1, Permutation([1, 2, 0]))] a = Permutation(range(1, 100) + [0]) G = PermutationGroup([a]) assert [min(o) for o in G.orbits()] == [0] G = PermutationGroup(rubik_cube_generators()) assert [min(o) for o in G.orbits()] == [0, 1] assert not G.is_transitive() and not G.is_transitive(strict=False) G = PermutationGroup([Permutation(0, 1, 3), Permutation(3)(0, 1)]) assert not G.is_transitive() and G.is_transitive(strict=False) assert PermutationGroup(Permutation(3)).is_transitive(strict=False) is False