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cosmetics
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@mantepse
mantepse committed Nov 13, 2024
1 parent cbf8b1d commit f4849ee
Showing 1 changed file with 47 additions and 57 deletions.
104 changes: 47 additions & 57 deletions src/sage/rings/lazy_species.py
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Original file line number Diff line number Diff line change
@@ -1,19 +1,27 @@
from sage.rings.integer_ring import ZZ
from sage.rings.lazy_series import LazyCompletionGradedAlgebraElement, LazyModuleElement
from sage.rings.lazy_series_ring import LazyCompletionGradedAlgebra
from sage.rings.lazy_series_ring import (LazyCompletionGradedAlgebra,
LazyPowerSeriesRing,
LazySymmetricFunctions)
from sage.rings.species import PolynomialSpecies
from sage.data_structures.stream import (Stream_zero,
Stream_exact,
Stream_function)
from sage.rings.species import PolynomialSpecies
from sage.libs.gap.libgap import libgap
from sage.categories.sets_cat import cartesian_product
from sage.categories.tensor import tensor
from sage.combinat.integer_vector import IntegerVectors
from sage.combinat.subset import subsets
from sage.combinat.sf.sf import SymmetricFunctions
from sage.combinat.partition import Partitions
from sage.combinat.permutation import CyclicPermutations
from sage.combinat.set_partition import SetPartitions
from sage.graphs.graph_generators import graphs
from sage.groups.perm_gps.permgroup_named import SymmetricGroup, CyclicPermutationGroup
from sage.libs.gap.libgap import libgap
from sage.structure.element import parent
import itertools
from collections import defaultdict
from sage.rings.lazy_series_ring import LazyPowerSeriesRing, LazySymmetricFunctions
from sage.combinat.sf.sf import SymmetricFunctions
from sage.groups.perm_gps.permgroup_named import SymmetricGroup


def weighted_compositions(n, d, weights, offset=0):
r"""
Expand Down Expand Up @@ -114,6 +122,7 @@ def label_sets(arity, labels):

######################################################################


class LazySpeciesElement(LazyCompletionGradedAlgebraElement):
r"""
Expand Down Expand Up @@ -271,14 +280,17 @@ def cycle_index_series(self):
p = SymmetricFunctions(P.base_ring().fraction_field()).p()
if P._arity == 1:
L = LazySymmetricFunctions(p)

def coefficient(n):
return sum(c * M.permutation_group()[0].cycle_index()
for M, c in self[n].monomial_coefficients().items())
else:
L = LazySymmetricFunctions(tensor([p for _ in range(P._arity)]))

def coefficient(n):
return sum(c * M.cycle_index()
for M, c in self[n].monomial_coefficients().items())

return L(coefficient)

def _add_(self, other):
Expand Down Expand Up @@ -314,14 +326,15 @@ def _mul_(self, other):
sage: from sage.rings.lazy_species import LazySpecies
sage: L = LazySpecies(ZZ, "X")
sage: E = L(lambda n: SymmetricGroup(n))
sage: list((E^2).structures([1,2,3]))
sage: sorted((E^2).structures([1,2,3]))
[(((), 1), ((1, 2, 3), E_3)),
(((1,), X), ((2, 3), E_2)),
(((2,), X), ((1, 3), E_2)),
(((3,), X), ((1, 2), E_2)),
(((1, 2), E_2), ((3,), X)),
(((1, 2, 3), E_3), ((), 1)),
(((1, 3), E_2), ((2,), X)),
(((2, 3), E_2), ((1,), X))]
(((2,), X), ((1, 3), E_2)),
(((2, 3), E_2), ((1,), X)),
(((3,), X), ((1, 2), E_2))]
"""
return ProductSpeciesElement(self, other)

Expand All @@ -348,31 +361,31 @@ def structures(self, *labels):
[((1, 2, 3), C_3), ((2, 1, 3), C_3)]
sage: F = 1/(2-E)
sage: list(F.structures([1,2,3]))
sage: sorted(F.structures([1,2,3]))
[((1, 2, 3), E_3),
((1, 2, 3), X*E_2, 0),
((3, 2, 1), X*E_2, 0),
((2, 3, 1), X*E_2, 0),
((1, 2, 3), X*E_2, 1),
((3, 2, 1), X*E_2, 1),
((2, 3, 1), X*E_2, 1),
((1, 2, 3), X^3),
((3, 2, 1), X^3),
((3, 1, 2), X^3),
((1, 3, 2), X^3),
((2, 1, 3), X^3),
((2, 3, 1), X*E_2, 0),
((2, 3, 1), X*E_2, 1),
((2, 3, 1), X^3),
((1, 3, 2), X^3)]
((3, 1, 2), X*E_2, 0),
((3, 1, 2), X*E_2, 1),
((3, 1, 2), X^3),
((3, 2, 1), X^3)]
sage: from sage.rings.species import PolynomialSpecies
sage: L2 = LazySpecies(QQ, "X, Y")
sage: P2 = PolynomialSpecies(QQ, "X, Y")
sage: XY = L2(P2(PermutationGroup([], domain=[1, 2]), {0: [1], 1: [2]}))
sage: L = LazySpecies(QQ, "X, Y")
sage: P = PolynomialSpecies(QQ, "X, Y")
sage: XY = L(P(PermutationGroup([], domain=[1, 2]), {0: [1], 1: [2]}))
sage: list((XY).structures([1], [2]))
[((1, 2), X*Y)]
sage: list(E(XY).structures([1,2],[3,4]))
[((3, 4, 1, 2), {((1,2)(3,4),): ({1, 2}, {3, 4})}),
((4, 3, 1, 2), {((1,2)(3,4),): ({1, 2}, {3, 4})})]
[((1, 2, 3, 4), {((1,2)(3,4),): ({1, 2}, {3, 4})}),
((2, 1, 3, 4), {((1,2)(3,4),): ({1, 2}, {3, 4})})]
sage: list(XY.structures([], [1, 2]))
[]
Expand Down Expand Up @@ -466,18 +479,8 @@ def __call__(self, *args):
sage: E = L(lambda n: SymmetricGroup(n))
sage: A = L.undefined(1)
sage: A.define(X*E(A))
sage: A
X + X^2 + (X^3+X*E_2) + (X^2*E_2+2*X^4+X*E_3)
+ (X^2*E_3+3*X^5+3*X^3*E_2+X*{((1,2)(3,4),)}+X*E_4)
+ (X^2*E_4+2*X^2*{((1,2)(3,4),)}+6*X^4*E_2+6*X^6
+3*X^3*E_3+E_2^2*X^2+X*E_5)
+ (X^2*E_5+2*E_2^2*X^3+6*X^4*E_3+12*X^7+14*X^5*E_2
+3*X^3*{((1,2)(3,4),)}+3*X^3*E_4
+X*{((3,4),(1,2),(1,3)(2,4)(5,6))}
+X*{((1,2)(3,4)(5,6),)}
+X*{((1,2)(4,5),(1,2,3)(4,5,6))}
+2*E_2*X^2*E_3+E_2*{((1,2)(3,4),)}*X+X*E_6)
+ O^8
sage: A[5]
X*E_4 + X^2*E_3 + 3*X^3*E_2 + X*{((1,2)(3,4),)} + 3*X^5
sage: C = L(lambda n: CyclicPermutationGroup(n) if n else 0)
sage: F = E(C(A))
Expand All @@ -491,15 +494,8 @@ def __call__(self, *args):
sage: L = LazySpecies(R, "X")
sage: E = L(lambda n: SymmetricGroup(n))
sage: E1 = L(lambda n: SymmetricGroup(n) if n else 0)
sage: E(q*E1)
1 + q*X + ((q^2+q)*E_2) + ((q^3+q)*E_3+q^2*X*E_2)
+ ((q^4+q)*E_4+q^2*P_4+q^2*X*E_3+q^3*E_2^2)
+ ((q^5+q)*E_5+(q^4+q^3+q^2)*E_2*E_3+q^2*X*E_4+q^3*X*P_4)
+ ((q^6+q)*E_6+q^2*{((1,2,3)(4,6),(1,4)(2,5)(3,6))}
+(q^5+q^3+q^2)*E_2*E_4+q^2*X*E_5
+q^3*{((1,4)(2,3),(1,6,3,2,5,4))}
+q^3*X*E_2*E_3+q^4*E_2*P_4+q^4*E_3^2)
+ O^7
sage: E(q*E1)[4]
(q^4+q)*E_4 + q^2*P_4 + q^2*X*E_3 + q^3*E_2^2
TESTS::
Expand Down Expand Up @@ -544,8 +540,7 @@ def structures(self, *labels):
yield from self._left.structures(*labels)
yield from self._right.structures(*labels)

from itertools import chain, product
from sage.combinat.subset import subsets

class ProductSpeciesElement(LazySpeciesElement):
def __init__(self, left, right):
self._left = left
Expand Down Expand Up @@ -579,9 +574,10 @@ def dissections(s):
yield (subset, s - subset)

labels = label_sets(self.parent()._arity, labels)
for d in product(*[dissections(u) for u in labels]):
yield from product(self._left.structures(*[U for U, _ in d]),
self._right.structures(*[V for _, V in d]))
for d in itertools.product(*[dissections(u) for u in labels]):
yield from itertools.product(self._left.structures(*[U for U, _ in d]),
self._right.structures(*[V for _, V in d]))


class CompositionSpeciesElement(LazySpeciesElement):
def __init__(self, left, *args):
Expand Down Expand Up @@ -727,7 +723,6 @@ def __init__(self, base_ring, names, sparse):
self.Cycles = lambda: CycleSpecies(self)


from sage.groups.perm_gps.permgroup_named import SymmetricGroup
class SetSpecies(LazySpeciesElement):
def __init__(self, parent):
P = parent._laurent_poly_ring
Expand All @@ -748,8 +743,7 @@ def structures(self, *labels):
labels = label_sets(self.parent()._arity, labels)
yield labels[0]

from sage.groups.perm_gps.permgroup_named import CyclicPermutationGroup
from sage.combinat.permutation import CyclicPermutations

class CycleSpecies(LazySpeciesElement):
def __init__(self, parent):
P = parent._laurent_poly_ring
Expand All @@ -776,8 +770,7 @@ def structures(self, *labels):
labels = label_sets(self.parent()._arity, labels)
yield from CyclicPermutations(labels[0])

from sage.graphs.graph_generators import graphs
from sage.rings.integer_ring import ZZ

class GraphSpecies(LazySpeciesElement):
def __init__(self, parent):
P = parent._laurent_poly_ring
Expand All @@ -789,9 +782,6 @@ def isotypes(self, labels):
yield from graphs(labels)


from sage.combinat.partition import Partitions
from sage.groups.perm_gps.permgroup_named import SymmetricGroup
from sage.combinat.set_partition import SetPartitions
class SetPartitionSpecies(LazySpeciesElement):
def __init__(self, parent):
P = parent._laurent_poly_ring
Expand Down

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