"""Test groups defined by the galois module. """

from sympy.combinatorics.galois import (
    S4TransitiveSubgroups, S5TransitiveSubgroups, S6TransitiveSubgroups,
    find_transitive_subgroups_of_S6,
)
from sympy.combinatorics.homomorphisms import is_isomorphic
from sympy.combinatorics.named_groups import (
    SymmetricGroup, AlternatingGroup, CyclicGroup,
)


def test_four_group():
    G = S4TransitiveSubgroups.V.get_perm_group()
    A4 = AlternatingGroup(4)
    assert G.is_subgroup(A4)
    assert G.degree == 4
    assert G.is_transitive()
    assert G.order() == 4
    assert not G.is_cyclic


def test_M20():
    G = S5TransitiveSubgroups.M20.get_perm_group()
    S5 = SymmetricGroup(5)
    A5 = AlternatingGroup(5)
    assert G.is_subgroup(S5)
    assert not G.is_subgroup(A5)
    assert G.degree == 5
    assert G.is_transitive()
    assert G.order() == 20


# Setting this True means that for each of the transitive subgroups of S6,
# we run a test not only on the fixed representation, but also on one freshly
# generated by the search procedure.
INCLUDE_SEARCH_REPS = False
S6_randomized = {}
if INCLUDE_SEARCH_REPS:
    S6_randomized = find_transitive_subgroups_of_S6(*list(S6TransitiveSubgroups))


def get_versions_of_S6_subgroup(name):
    vers = [name.get_perm_group()]
    if INCLUDE_SEARCH_REPS:
        vers.append(S6_randomized[name])
    return vers


def test_S6_transitive_subgroups():
    """
    Test enough characteristics to distinguish all 16 transitive subgroups.
    """
    ts = S6TransitiveSubgroups
    A6 = AlternatingGroup(6)
    for name, alt, order, is_isom, not_isom in [
        (ts.C6,     False,    6, CyclicGroup(6), None),
        (ts.S3,     False,    6, SymmetricGroup(3), None),
        (ts.D6,     False,   12, None, None),
        (ts.A4,     True,    12, None, None),
        (ts.G18,    False,   18, None, None),
        (ts.A4xC2,  False,   24, None, SymmetricGroup(4)),
        (ts.S4m,    False,   24, SymmetricGroup(4), None),
        (ts.S4p,    True,    24, None, None),
        (ts.G36m,   False,   36, None, None),
        (ts.G36p,   True,    36, None, None),
        (ts.S4xC2,  False,   48, None, None),
        (ts.PSL2F5, True,    60, None, None),
        (ts.G72,    False,   72, None, None),
        (ts.PGL2F5, False,  120, None, None),
        (ts.A6,     True,   360, None, None),
        (ts.S6,     False,  720, None, None),
    ]:
        for G in get_versions_of_S6_subgroup(name):
            assert G.is_transitive()
            assert G.degree == 6
            assert G.is_subgroup(A6) is alt
            assert G.order() == order
            if is_isom:
                assert is_isomorphic(G, is_isom)
            if not_isom:
                assert not is_isomorphic(G, not_isom)