def test_schreier_graph_construction(self):
s1 = Permutation.read_cycle_form([[2,3]], 4)
s2 = Permutation.read_cycle_form([[1,2,4]], 4)
gens = [s1,s2]
identity = Permutation([1,2,3,4])
s_g = _schreier_graph(2, gens, identity)
self.assertEqual(s_g, [s2,identity,s1,s2])
def test_coset_reps(self):
s1 = Permutation.read_cycle_form([[2,3]], 4)
s2 = Permutation.read_cycle_form([[1,2,4]], 4)
gens = [s1,s2]
identity = Permutation([1,2,3,4])
s_g = _schreier_graph(2, gens, identity)
cosets = _coset_reps(s_g, identity)
self.assertEqual(cosets, [Permutation.read_cycle_form([[1,4,2]], 4),identity,s1,s2])
def test_schreier_generators(self):
s1 = Permutation.read_cycle_form([[2,3]], 4)
s2 = Permutation.read_cycle_form([[1,2,4]], 4)
gens = [s1,s2]
identity = Permutation([1,2,3,4])
s_g = _schreier_graph(2, gens, identity)
cosets = _coset_reps(s_g, identity)
s_gen = _schreier_generators(2, cosets, gens, identity)
gen_1 = Permutation.read_cycle_form([[3,4]], 4)
gen_2 = Permutation.read_cycle_form([[1,3,4]], 4)
gen_3 = Permutation.read_cycle_form([[1,3]], 4)
self.assertEqual(s_gen, [gen_1, gen_2, gen_3])