Python SymmetricGroup.order Examples

Example #1

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

def test_sylow_subgroup():
    P = PermutationGroup(
        Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5))
    S = P.sylow_subgroup(2)
    assert S.order() == 4

    P = DihedralGroup(12)
    S = P.sylow_subgroup(3)
    assert S.order() == 3

    P = PermutationGroup(
        Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5),
        Permutation(0, 2))
    S = P.sylow_subgroup(3)
    assert S.order() == 9
    S = P.sylow_subgroup(2)
    assert S.order() == 8

    P = SymmetricGroup(10)
    S = P.sylow_subgroup(2)
    assert S.order() == 256
    S = P.sylow_subgroup(3)
    assert S.order() == 81
    S = P.sylow_subgroup(5)
    assert S.order() == 25

    # the length of the lower central series
    # of a p-Sylow subgroup of Sym(n) grows with
    # the highest exponent exp of p such
    # that n >= p**exp
    exp = 1
    length = 0
    for i in range(2, 9):
        P = SymmetricGroup(i)
        S = P.sylow_subgroup(2)
        ls = S.lower_central_series()
        if i // 2**exp > 0:
            # length increases with exponent
            assert len(ls) > length
            length = len(ls)
            exp += 1
        else:
            assert len(ls) == length

    G = SymmetricGroup(100)
    S = G.sylow_subgroup(3)
    assert G.order() % S.order() == 0
    assert G.order() / S.order() % 3 > 0

    G = AlternatingGroup(100)
    S = G.sylow_subgroup(2)
    assert G.order() % S.order() == 0
    assert G.order() / S.order() % 2 > 0

Example #2

File: test_named_groups.py Project: hector1618/sympy

def test_SymmetricGroup():
    G = SymmetricGroup(5)
    elements = list(G.generate())
    assert (G.generators[0]).size == 5
    assert len(elements) == 120
    assert G.is_solvable() == False
    assert G.is_abelian == False
    assert G.is_transitive == True
    H = SymmetricGroup(1)
    assert H.order() == 1
    L = SymmetricGroup(2)
    assert L.order() == 2

Example #3

File: test_named_groups.py Project: vperic/sympy

def test_SymmetricGroup():
    G = SymmetricGroup(5)
    elements = list(G.generate())
    assert (G.generators[0]).size == 5
    assert len(elements) == 120
    assert G.is_solvable() == False
    assert G.is_abelian == False
    assert G.is_transitive == True
    H = SymmetricGroup(1)
    assert H.order() == 1
    L = SymmetricGroup(2)
    assert L.order() == 2

Example #4

File: test_perm_groups.py Project: baoqchau/sympy

def test_sylow_subgroup():
    P = PermutationGroup(Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5))
    S = P.sylow_subgroup(2)
    assert S.order() == 4

    P = DihedralGroup(12)
    S = P.sylow_subgroup(3)
    assert S.order() == 3

    P = PermutationGroup(Permutation(1, 5)(2, 4), Permutation(0, 1, 2, 3, 4, 5), Permutation(0, 2))
    S = P.sylow_subgroup(3)
    assert S.order() == 9
    S = P.sylow_subgroup(2)
    assert S.order() == 8

    P = SymmetricGroup(10)
    S = P.sylow_subgroup(2)
    assert S.order() == 256
    S = P.sylow_subgroup(3)
    assert S.order() == 81
    S = P.sylow_subgroup(5)
    assert S.order() == 25

    # the length of the lower central series
    # of a p-Sylow subgroup of Sym(n) grows with
    # the highest exponent exp of p such
    # that n >= p**exp
    exp = 1
    length = 0
    for i in range(2, 9):
        P = SymmetricGroup(i)
        S = P.sylow_subgroup(2)
        ls = S.lower_central_series()
        if i // 2**exp > 0:
            # length increases with exponent
            assert len(ls) > length
            length = len(ls)
            exp += 1
        else:
            assert len(ls) == length

    G = SymmetricGroup(100)
    S = G.sylow_subgroup(3)
    assert G.order() % S.order() == 0
    assert G.order()/S.order() % 3 > 0

    G = AlternatingGroup(100)
    S = G.sylow_subgroup(2)
    assert G.order() % S.order() == 0
    assert G.order()/S.order() % 2 > 0

Example #5

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 #6

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