Python _verify_bsgs Examples

Example #1

File: test_testutil.py Project: Azatik1000/Massey-Omura-Cryptosystem

def test_verify_bsgs():
    S = SymmetricGroup(5)
    S.schreier_sims()
    base = S.base
    strong_gens = S.strong_gens
    assert _verify_bsgs(S, base, strong_gens) is True
    assert _verify_bsgs(S, base[:-1], strong_gens) is False
    assert _verify_bsgs(S, base, S.generators) is False

Example #2

File: 55040_test_perm_groups.py Project: tate11/intelligent-code-completion

def test_baseswap():
    S = SymmetricGroup(4)
    S.schreier_sims()
    base = S.base
    strong_gens = S.strong_gens
    assert base == [0, 1, 2]
    deterministic = S.baseswap(base, strong_gens, 1, randomized=False)
    randomized = S.baseswap(base, strong_gens, 1)
    assert deterministic[0] == [0, 2, 1]
    assert _verify_bsgs(S, deterministic[0], deterministic[1]) is True
    assert randomized[0] == [0, 2, 1]
    assert _verify_bsgs(S, randomized[0], randomized[1]) is True

Example #3

File: test_perm_groups.py Project: sixpearls/sympy

def test_baseswap():
    S = SymmetricGroup(4)
    S.schreier_sims()
    base = S.base
    strong_gens = S.strong_gens
    assert base == [0, 1, 2]
    deterministic = S.baseswap(base, strong_gens, 1, randomized=False)
    randomized = S.baseswap(base, strong_gens, 1)
    assert deterministic[0] == [0, 2, 1]
    assert _verify_bsgs(S, deterministic[0], deterministic[1]) is True
    assert randomized[0] == [0, 2, 1]
    assert _verify_bsgs(S, randomized[0], randomized[1]) is True

Example #4

File: test_util.py Project: jenshnielsen/sympy

def test_remove_gens():
    S = SymmetricGroup(10)
    base, strong_gens = S.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(S, base, new_gens) is True
    A = AlternatingGroup(7)
    base, strong_gens = A.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(A, base, new_gens) is True
    D = DihedralGroup(2)
    base, strong_gens = D.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(D, base, new_gens) is True

Example #5

def test_remove_gens():
    S = SymmetricGroup(10)
    base, strong_gens = S.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(S, base, new_gens) == True
    A = AlternatingGroup(7)
    base, strong_gens = A.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(A, base, new_gens) == True
    D = DihedralGroup(2)
    base, strong_gens = D.schreier_sims_incremental()
    new_gens = _remove_gens(base, strong_gens)
    assert _verify_bsgs(D, base, new_gens) == True

Example #6

File: 55040_test_perm_groups.py Project: tate11/intelligent-code-completion

def _subgroup_search(i, j, k):
    prop_true = lambda x: True
    prop_fix_points = lambda x: [x(point) for point in points] == points
    prop_comm_g = lambda x: rmul(x, g) == rmul(g, x)
    prop_even = lambda x: x.is_even
    for i in range(i, j, k):
        S = SymmetricGroup(i)
        A = AlternatingGroup(i)
        C = CyclicGroup(i)
        Sym = S.subgroup_search(prop_true)
        assert Sym.is_subgroup(S)
        Alt = S.subgroup_search(prop_even)
        assert Alt.is_subgroup(A)
        Sym = S.subgroup_search(prop_true, init_subgroup=C)
        assert Sym.is_subgroup(S)
        points = [7]
        assert S.stabilizer(7).is_subgroup(S.subgroup_search(prop_fix_points))
        points = [3, 4]
        assert S.stabilizer(3).stabilizer(4).is_subgroup(
            S.subgroup_search(prop_fix_points))
        points = [3, 5]
        fix35 = A.subgroup_search(prop_fix_points)
        points = [5]
        fix5 = A.subgroup_search(prop_fix_points)
        assert A.subgroup_search(prop_fix_points,
                                 init_subgroup=fix35).is_subgroup(fix5)
        base, strong_gens = A.schreier_sims_incremental()
        g = A.generators[0]
        comm_g = \
            A.subgroup_search(prop_comm_g, base=base, strong_gens=strong_gens)
        assert _verify_bsgs(comm_g, base, comm_g.generators) is True
        assert [prop_comm_g(gen) is True for gen in comm_g.generators]

Example #7

File: test_perm_groups.py Project: sixpearls/sympy

def _subgroup_search(i, j, k):
    prop_true = lambda x: True
    prop_fix_points = lambda x: [x(point) for point in points] == points
    prop_comm_g = lambda x: rmul(x, g) == rmul(g, x)
    prop_even = lambda x: x.is_even
    for i in range(i, j, k):
        S = SymmetricGroup(i)
        A = AlternatingGroup(i)
        C = CyclicGroup(i)
        Sym = S.subgroup_search(prop_true)
        assert Sym.is_subgroup(S)
        Alt = S.subgroup_search(prop_even)
        assert Alt.is_subgroup(A)
        Sym = S.subgroup_search(prop_true, init_subgroup=C)
        assert Sym.is_subgroup(S)
        points = [7]
        assert S.stabilizer(7).is_subgroup(S.subgroup_search(prop_fix_points))
        points = [3, 4]
        assert S.stabilizer(3).stabilizer(4).is_subgroup(
            S.subgroup_search(prop_fix_points))
        points = [3, 5]
        fix35 = A.subgroup_search(prop_fix_points)
        points = [5]
        fix5 = A.subgroup_search(prop_fix_points)
        assert A.subgroup_search(prop_fix_points, init_subgroup=fix35
            ).is_subgroup(fix5)
        base, strong_gens = A.schreier_sims_incremental()
        g = A.generators[0]
        comm_g = \
            A.subgroup_search(prop_comm_g, base=base, strong_gens=strong_gens)
        assert _verify_bsgs(comm_g, base, comm_g.generators) is True
        assert [prop_comm_g(gen) is True for gen in comm_g.generators]

Example #8

def test_subgroup_search():
    prop_true = lambda x: True
    prop_fix_points = lambda x: [x(point) for point in points] == points
    prop_comm_g = lambda x: x*g == g*x
    prop_even = lambda x: x.is_even
    for i in range(10, 17, 2):
        S = SymmetricGroup(i)
        A = AlternatingGroup(i)
        C = CyclicGroup(i)
        Sym = S.subgroup_search(prop_true)
        assert Sym == S
        Alt = S.subgroup_search(prop_even)
        assert Alt == A
        Sym = S.subgroup_search(prop_true, init_subgroup=C)
        assert Sym == S
        points = [7]
        assert S.stabilizer(7) == S.subgroup_search(prop_fix_points)
        points = [3, 4]
        assert S.stabilizer(3).stabilizer(4) ==\
               S.subgroup_search(prop_fix_points)
        points = [3, 5]
        fix35 = A.subgroup_search(prop_fix_points)
        points = [5]
        fix5 = A.subgroup_search(prop_fix_points)
        assert A.subgroup_search(prop_fix_points, init_subgroup=fix35) == fix5
        base, strong_gens = A.schreier_sims_incremental()
        g = A.generators[0]
        comm_g =\
             A.subgroup_search(prop_comm_g, base=base, strong_gens=strong_gens)
        assert _verify_bsgs(comm_g, base, comm_g.generators) == True
        assert [prop_comm_g(gen) == True for gen in comm_g.generators]

Example #9

File: 55040_test_perm_groups.py Project: tate11/intelligent-code-completion

def test_schreier_sims_incremental():
    identity = Permutation([0, 1, 2, 3, 4])
    TrivialGroup = PermutationGroup([identity])
    base, strong_gens = TrivialGroup.schreier_sims_incremental(base=[0, 1, 2])
    assert _verify_bsgs(TrivialGroup, base, strong_gens) is True
    S = SymmetricGroup(5)
    base, strong_gens = S.schreier_sims_incremental(base=[0, 1, 2])
    assert _verify_bsgs(S, base, strong_gens) is True
    D = DihedralGroup(2)
    base, strong_gens = D.schreier_sims_incremental(base=[1])
    assert _verify_bsgs(D, base, strong_gens) is True
    A = AlternatingGroup(7)
    gens = A.generators[:]
    gen0 = gens[0]
    gen1 = gens[1]
    gen1 = rmul(gen1, ~gen0)
    gen0 = rmul(gen0, gen1)
    gen1 = rmul(gen0, gen1)
    base, strong_gens = A.schreier_sims_incremental(base=[0, 1], gens=gens)
    assert _verify_bsgs(A, base, strong_gens) is True
    C = CyclicGroup(11)
    gen = C.generators[0]
    base, strong_gens = C.schreier_sims_incremental(gens=[gen**3])
    assert _verify_bsgs(C, base, strong_gens) is True

Example #10

File: test_perm_groups.py Project: sixpearls/sympy

def test_schreier_sims_incremental():
    identity = Permutation([0, 1, 2, 3, 4])
    TrivialGroup = PermutationGroup([identity])
    base, strong_gens = TrivialGroup.schreier_sims_incremental(base=[0, 1, 2])
    assert _verify_bsgs(TrivialGroup, base, strong_gens) is True
    S = SymmetricGroup(5)
    base, strong_gens = S.schreier_sims_incremental(base=[0, 1, 2])
    assert _verify_bsgs(S, base, strong_gens) is True
    D = DihedralGroup(2)
    base, strong_gens = D.schreier_sims_incremental(base=[1])
    assert _verify_bsgs(D, base, strong_gens) is True
    A = AlternatingGroup(7)
    gens = A.generators[:]
    gen0 = gens[0]
    gen1 = gens[1]
    gen1 = rmul(gen1, ~gen0)
    gen0 = rmul(gen0, gen1)
    gen1 = rmul(gen0, gen1)
    base, strong_gens = A.schreier_sims_incremental(base=[0, 1], gens=gens)
    assert _verify_bsgs(A, base, strong_gens) is True
    C = CyclicGroup(11)
    gen = C.generators[0]
    base, strong_gens = C.schreier_sims_incremental(gens=[gen**3])
    assert _verify_bsgs(C, base, strong_gens) is True