def test_generate():
a = Permutation([1, 0])
g = list(PermutationGroup([a]).generate())
assert g == [Permutation([0, 1]), Permutation([1, 0])]
assert len(list(PermutationGroup(Permutation((0, 1))).generate())) == 1
g = PermutationGroup([a]).generate(method='dimino')
assert list(g) == [Permutation([0, 1]), Permutation([1, 0])]
a = Permutation([2, 0, 1])
b = Permutation([2, 1, 0])
G = PermutationGroup([a, b])
g = G.generate()
v1 = [p.array_form for p in list(g)]
v1.sort()
assert v1 == [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0, 1],
[2, 1, 0]]
v2 = list(G.generate(method='dimino', af=True))
assert v1 == sorted(v2)
a = Permutation([2, 0, 1, 3, 4, 5])
b = Permutation([2, 1, 3, 4, 5, 0])
g = PermutationGroup([a, b]).generate(af=True)
assert len(list(g)) == 360
def test_generate():
a = Permutation([1, 0])
g = list(PermutationGroup([a]).generate())
assert g == [Permutation([0, 1]), Permutation([1, 0])]
assert len(list(PermutationGroup(Permutation((0, 1))).generate())) == 1
g = PermutationGroup([a]).generate(method='dimino')
assert list(g) == [Permutation([0, 1]), Permutation([1, 0])]
a = Permutation([2, 0, 1])
b = Permutation([2, 1, 0])
G = PermutationGroup([a, b])
g = G.generate()
v1 = [p.array_form for p in list(g)]
v1.sort()
assert v1 == [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0,
1], [2, 1, 0]]
v2 = list(G.generate(method='dimino', af=True))
assert v1 == sorted(v2)
a = Permutation([2, 0, 1, 3, 4, 5])
b = Permutation([2, 1, 3, 4, 5, 0])
g = PermutationGroup([a, b]).generate(af=True)
assert len(list(g)) == 360
def test_coset_rank():
gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]]
gens = [Permutation(p) for p in gens_cube]
G = PermutationGroup(gens)
i = 0
for h in G.generate(af=True):
rk = G.coset_rank(h)
assert rk == i
h1 = G.coset_unrank(rk, af=True)
assert h == h1
i += 1
assert G.coset_unrank(48) is None
assert G.coset_unrank(G.coset_rank(gens[0])) == gens[0]
def test_coset_rank():
gens_cube = [[1, 3, 5, 7, 0, 2, 4, 6], [1, 3, 0, 2, 5, 7, 4, 6]]
gens = [Permutation(p) for p in gens_cube]
G = PermutationGroup(gens)
i = 0
for h in G.generate(af=True):
rk = G.coset_rank(h)
assert rk == i
h1 = G.coset_unrank(rk, af=True)
assert h == h1
i += 1
assert G.coset_unrank(48) is None
assert G.coset_unrank(G.coset_rank(gens[0])) == gens[0]
def canonicalize_naive(g, dummies, sym, *v):
"""
Canonicalize tensor formed by tensors of the different types
g permutation representing the tensor
dummies list of dummy indices
msym symmetry of the metric
v is a list of (base_i, gens_i, n_i, sym_i) for tensors of type `i`
base_i, gens_i BSGS for tensors of this type
n_i number ot tensors of type `i`
sym_i symmetry under exchange of two component tensors of type `i`
None no symmetry
0 commuting
1 anticommuting
Return 0 if the tensor is zero, else return the array form of
the permutation representing the canonical form of the tensor.
Examples
========
>>> from diofant.combinatorics.testutil import canonicalize_naive
>>> from diofant.combinatorics.tensor_can import get_symmetric_group_sgs
>>> from diofant.combinatorics import Permutation, PermutationGroup
>>> g = Permutation([1, 3, 2, 0, 4, 5])
>>> base2, gens2 = get_symmetric_group_sgs(2)
>>> canonicalize_naive(g, [2, 3], 0, (base2, gens2, 2, 0))
[0, 2, 1, 3, 4, 5]
"""
from diofant.combinatorics.perm_groups import PermutationGroup
from diofant.combinatorics.tensor_can import gens_products, dummy_sgs
from diofant.combinatorics.permutations import Permutation, _af_rmul
v1 = []
for i in range(len(v)):
base_i, gens_i, n_i, sym_i = v[i]
v1.append((base_i, gens_i, [[]]*n_i, sym_i))
size, sbase, sgens = gens_products(*v1)
dgens = dummy_sgs(dummies, sym, size-2)
if isinstance(sym, int):
num_types = 1
dummies = [dummies]
sym = [sym]
else:
num_types = len(sym)
dgens = []
for i in range(num_types):
dgens.extend(dummy_sgs(dummies[i], sym[i], size - 2))
S = PermutationGroup(sgens)
D = PermutationGroup([Permutation(x) for x in dgens])
dlist = list(D.generate(af=True))
g = g.array_form
st = set()
for s in S.generate(af=True):
h = _af_rmul(g, s)
for d in dlist:
q = tuple(_af_rmul(d, h))
st.add(q)
a = list(st)
a.sort()
prev = (0,)*size
for h in a:
if h[:-2] == prev[:-2]:
if h[-1] != prev[-1]:
return 0
prev = h
return list(a[0])