Python SymmetricGroup.schreier_sims 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_orbits_transversals_from_bsgs():
    S = SymmetricGroup(4)
    S.schreier_sims()
    base = S.base
    strong_gens = S.strong_gens
    strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
    result = _orbits_transversals_from_bsgs(base, strong_gens_distr)
    orbits = result[0]
    transversals = result[1]
    base_len = len(base)
    for i in range(base_len):
        for el in orbits[i]:
            assert transversals[i][el](base[i]) == el
            for j in range(i):
                assert transversals[i][el](base[j]) == base[j]
    order = 1
    for i in range(base_len):
        order *= len(orbits[i])
    assert S.order() == order

Example #5

def test_orbits_transversals_from_bsgs():
    S = SymmetricGroup(4)
    S.schreier_sims()
    base = S.base
    strong_gens = S.strong_gens
    strong_gens_distr = _distribute_gens_by_base(base, strong_gens)
    result = _orbits_transversals_from_bsgs(base, strong_gens_distr)
    orbits = result[0]
    transversals = result[1]
    base_len = len(base)
    for i in range(base_len):
        for el in orbits[i]:
            assert transversals[i][el](base[i]) == el
            for j in range(i):
                assert transversals[i][el](base[j]) == base[j]
    order = 1
    for i in range(base_len):
        order *= len(orbits[i])
    assert S.order() == order