def test_schreier_sims_algorithm(self):
cf =Permutation.read_cycle_form
a = cf([[1, 2]],4)
b = cf([[1,2,3,4]], 4)
c = cf([[2, 3, 4]], 4)
d = cf([[2, 3]], 4)
e = cf([], 4)
info = schreier_sims_algorithm([], e)
self.assertEquals(info, ([],[],[],[]))
info = schreier_sims_algorithm([e,e,e,e], e)
self.assertEquals(info, ([],[],[],[]))
base, gens, c_gens, graphs = schreier_sims_algorithm([a,b], e)
self.assertEquals(len(base), 3)
def coset_construction_from_schreier_tree_test(self, gens):
identity = gens[0] * gens[0]**-1
base, strong_gens, chain_generators, schreier_graphs = schreier_sims_algorithm(gens, identity)
no_errors = True
for s_g in schreier_graphs[0:-1]:
coset_inverses_1 = _coset_rep_inverses(s_g, identity)
coset_inverses_2 = [_coset_rep_inverse(i + 1, s_g, identity) for i in range(len(identity))]
if coset_inverses_1 != coset_inverses_2:
no_errors = False
print(coset_inverses_1)
print(coset_inverses_2)
self.assertTrue(no_errors)
def __init__(self, generators, schreier_sims_info = None):
self.generators = generators
if len(generators) > 0:
g = self.generators[0]
self.identity = g**-1 * g
else:
self.identity = Permutation([1])
if schreier_sims_info is None:
b, strong_gens, chain_gens, sgs = schreier_sims_tools.schreier_sims_algorithm(self.generators, self.identity)
else:
b, strong_gens, chain_gens, sgs = schreier_sims_info
self.base = b
self.strong_generators = strong_gens
self.chain_generators = chain_gens
self.schreier_graphs = sgs