def test_schreier_vector():
    G = CyclicGroup(50)
    v = [0]*50
    v[23] = -1
    assert G.schreier_vector(23) == v
    H = DihedralGroup(8)
    assert H.schreier_vector(2) == [0, 1, -1, 0, 0, 1, 0, 0]
    L = SymmetricGroup(4)
    assert L.schreier_vector(1) == [1, -1, 0, 0]

def test_CyclicGroup():
    G = CyclicGroup(10)
    elements = list(G.generate())
    assert len(elements) == 10
    assert (G.commutator()).order() == 1
    assert G.is_abelian == True
    H = CyclicGroup(1)
    assert H.order() == 1
    L = CyclicGroup(2)
    assert L.order() == 2

def test_CyclicGroup():
    G = CyclicGroup(10)
    elements = list(G.generate())
    assert len(elements) == 10
    assert (G.derived_subgroup()).order() == 1
    assert G.is_abelian is True
    H = CyclicGroup(1)
    assert H.order() == 1
    L = CyclicGroup(2)
    assert L.order() == 2

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

def test_is_primitive():
    S = SymmetricGroup(5)
    assert S.is_primitive() is True
    C = CyclicGroup(7)
    assert C.is_primitive() is True

def test_orbit_rep():
    G = DihedralGroup(6)
    assert G.orbit_rep(1, 3) in [Permutation([2, 3, 4, 5, 0, 1]),
    Permutation([4, 3, 2, 1, 0, 5])]
    H = CyclicGroup(4)*G
    assert H.orbit_rep(1, 5) is False