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]
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]
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]
