def test_Permutation_Cycle():
from sympy.combinatorics import Permutation, Cycle
# general principle: economically, canonically show all moved elements
# and the size of the permutation.
for p, s in [
(Cycle(),
'()'),
(Cycle(2),
'(2)'),
(Cycle(2, 1),
'(1 2)'),
(Cycle(1, 2)(5)(6, 7)(10),
'(1 2)(6 7)(10)'),
(Cycle(3, 4)(1, 2)(3, 4),
'(1 2)(4)'),
]:
assert str(p) == s
Permutation.print_cyclic = False
for p, s in [
(Permutation([]),
'Permutation([])'),
(Permutation([], size=1),
'Permutation([0])'),
(Permutation([], size=2),
'Permutation([0, 1])'),
(Permutation([], size=10),
'Permutation([], size=10)'),
(Permutation([1, 0, 2]),
'Permutation([1, 0, 2])'),
(Permutation([1, 0, 2, 3, 4, 5]),
'Permutation([1, 0], size=6)'),
(Permutation([1, 0, 2, 3, 4, 5], size=10),
'Permutation([1, 0], size=10)'),
]:
assert str(p) == s
Permutation.print_cyclic = True
for p, s in [
(Permutation([]),
'()'),
(Permutation([], size=1),
'(0)'),
(Permutation([], size=2),
'(1)'),
(Permutation([], size=10),
'(9)'),
(Permutation([1, 0, 2]),
'(2)(0 1)'),
(Permutation([1, 0, 2, 3, 4, 5]),
'(5)(0 1)'),
(Permutation([1, 0, 2, 3, 4, 5], size=10),
'(9)(0 1)'),
(Permutation([0, 1, 3, 2, 4, 5], size=10),
'(9)(2 3)'),
]:
assert str(p) == s
def test_Permutation_Cycle():
from sympy.combinatorics import Permutation, Cycle
# general principle: economically, canonically show all moved elements
# and the size of the permutation.
for p, s in [
(Cycle(), "()"),
(Cycle(2), "(2)"),
(Cycle(2, 1), "(1 2)"),
(Cycle(1, 2)(5)(6, 7)(10), "(1 2)(6 7)(10)"),
(Cycle(3, 4)(1, 2)(3, 4), "(1 2)(4)"),
]:
assert sstr(p) == s
for p, s in [
(Permutation([]), "Permutation([])"),
(Permutation([], size=1), "Permutation([0])"),
(Permutation([], size=2), "Permutation([0, 1])"),
(Permutation([], size=10), "Permutation([], size=10)"),
(Permutation([1, 0, 2]), "Permutation([1, 0, 2])"),
(Permutation([1, 0, 2, 3, 4, 5]), "Permutation([1, 0], size=6)"),
(Permutation([1, 0, 2, 3, 4, 5],
size=10), "Permutation([1, 0], size=10)"),
]:
assert sstr(p, perm_cyclic=False) == s
for p, s in [
(Permutation([]), "()"),
(Permutation([], size=1), "(0)"),
(Permutation([], size=2), "(1)"),
(Permutation([], size=10), "(9)"),
(Permutation([1, 0, 2]), "(2)(0 1)"),
(Permutation([1, 0, 2, 3, 4, 5]), "(5)(0 1)"),
(Permutation([1, 0, 2, 3, 4, 5], size=10), "(9)(0 1)"),
(Permutation([0, 1, 3, 2, 4, 5], size=10), "(9)(2 3)"),
]:
assert sstr(p) == s
def test_Cycle():
# FIXME: sT fails because Cycle is not immutable and calling srepr(Cycle(1, 2))
# adds keys to the Cycle dict (GH-17661)
#import_stmt = "from sympy.combinatorics import Cycle"
#sT(Cycle(1, 2), "Cycle(1, 2)", import_stmt)
assert srepr(Cycle(1, 2)) == "Cycle(1, 2)"
from sympy.combinatorics import Permutation, Cycle
from sympy.combinatorics.named_groups import SymmetricGroup
S5 = SymmetricGroup(5)
S5_elems = list(S5.generate_schreier_sims())
IDENTITY = Permutation(4)
ALPHA = Permutation(Cycle(0, 1, 2, 3, 4))
BETA = Permutation(Cycle(0, 2, 4, 3, 1))
ALPHA_INV = (~ALPHA)
BETA_INV = (~BETA)
COMMUTATOR = ALPHA * BETA * ALPHA_INV * BETA_INV
ELEMENTS = [ALPHA, ALPHA_INV, BETA, BETA_INV, COMMUTATOR]
CONJUGATORS = {e: {} for e in ELEMENTS}
for e1 in ELEMENTS:
for e2 in ELEMENTS:
for gamma in S5_elems:
if gamma * e1 * (~gamma) == e2:
CONJUGATORS[e1][e2] = (gamma, ~gamma)
break
class GroupInstruction(object):
def __init__(self, index, g0, g1):
self.index = index
self.g0 = g0
self.g1 = g1
def __str__(self):
return str(self.index).ljust(4) + str(self.g0).ljust(15) + str(
self.g1).ljust(13)