def test_dummy_sgs():
a = dummy_sgs([1,2], 0, 4)
assert a == [[0,2,1,3,4,5]]
a = dummy_sgs([2,3,4,5], 0, 8)
assert a == [x._array_form for x in [Perm(9)(2,3), Perm(9)(4,5),
Perm(9)(2,4)(3,5)]]
a = dummy_sgs([2,3,4,5], 1, 8)
assert a == [x._array_form for x in [Perm(2,3)(8,9), Perm(4,5)(8,9),
Perm(9)(2,4)(3,5)]]
def test_dummy_sgs():
a = dummy_sgs([1,2], 0, 4)
assert a == [[0,2,1,3,4,5]]
a = dummy_sgs([2,3,4,5], 0, 8)
assert a == [x._array_form for x in [Perm(9)(2,3), Perm(9)(4,5),
Perm(9)(2,4)(3,5)]]
a = dummy_sgs([2,3,4,5], 1, 8)
assert a == [x._array_form for x in [Perm(2,3)(8,9), Perm(4,5)(8,9),
Perm(9)(2,4)(3,5)]]
def canonicalize_naive(g, dummies, sym, *v):
"""
Canonicalize tensor formed by tensors of the different types.
Explanation
===========
sym_i symmetry under exchange of two component tensors of type `i`
None no symmetry
0 commuting
1 anticommuting
Parameters
==========
g : Permutation representing the tensor.
dummies : List of dummy indices.
msym : Symmetry of the metric.
v : 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`
Returns
=======
Returns 0 if the tensor is zero, else returns the array form of
the permutation representing the canonical form of the tensor.
Examples
========
>>> from sympy.combinatorics.testutil import canonicalize_naive
>>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs
>>> from sympy.combinatorics import Permutation
>>> 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 sympy.combinatorics.perm_groups import PermutationGroup
from sympy.combinatorics.tensor_can import gens_products, dummy_sgs
from sympy.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])
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 sympy.combinatorics.testutil import canonicalize_naive
>>> from sympy.combinatorics.tensor_can import get_symmetric_group_sgs
>>> from sympy.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 sympy.combinatorics.perm_groups import PermutationGroup
from sympy.combinatorics.tensor_can import gens_products, dummy_sgs
from sympy.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])
