Composition species¶
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class
sage.combinat.species.composition_species.
CompositionSpecies
(F, G, min=None, max=None, weight=None)¶ Bases:
sage.combinat.species.species.GenericCombinatorialSpecies
,sage.structure.unique_representation.UniqueRepresentation
Returns the composition of two species.
EXAMPLES:
sage: E = species.SetSpecies() sage: C = species.CycleSpecies() sage: S = E(C) sage: S.generating_series().coefficients(5) [1, 1, 1, 1, 1] sage: E(C) is S True
TESTS:
sage: E = species.SetSpecies(); C = species.CycleSpecies() sage: L = E(C) sage: c = L.generating_series().coefficients(3) sage: L._check() #False due to isomorphism types not being implemented False sage: L == loads(dumps(L)) True
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weight_ring
()¶ Returns the weight ring for this species. This is determined by asking Sage’s coercion model what the result is when you multiply (and add) elements of the weight rings for each of the operands.
EXAMPLES:
sage: E = species.SetSpecies(); C = species.CycleSpecies() sage: L = E(C) sage: L.weight_ring() Rational Field
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class
sage.combinat.species.composition_species.
CompositionSpeciesStructure
(parent, labels, pi, f, gs)¶ Bases:
sage.combinat.species.structure.GenericSpeciesStructure
TESTS:
sage: E = species.SetSpecies(); C = species.CycleSpecies() sage: L = E(C) sage: a = L.structures(['a','b','c']).random_element() sage: a == loads(dumps(a)) True
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change_labels
(labels)¶ Return a relabelled structure.
INPUT:
labels
, a list of labels.
OUTPUT:
A structure with the i-th label of self replaced with the i-th label of the list.
EXAMPLES:
sage: p = PermutationGroupElement((2,3)) sage: E = species.SetSpecies(); C = species.CycleSpecies() sage: L = E(C) sage: S = L.structures(['a','b','c']).list() sage: a = S[2]; a F-structure: {{'a', 'c'}, {'b'}}; G-structures: (('a', 'c'), ('b')) sage: a.change_labels([1,2,3]) F-structure: {{1, 3}, {2}}; G-structures: [(1, 3), (2)]
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transport
(perm)¶ EXAMPLES:
sage: p = PermutationGroupElement((2,3)) sage: E = species.SetSpecies(); C = species.CycleSpecies() sage: L = E(C) sage: S = L.structures(['a','b','c']).list() sage: a = S[2]; a F-structure: {{'a', 'c'}, {'b'}}; G-structures: (('a', 'c'), ('b')) sage: a.transport(p) F-structure: {{'a', 'b'}, {'c'}}; G-structures: (('a', 'c'), ('b'))
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sage.combinat.species.composition_species.
CompositionSpecies_class
¶ alias of
CompositionSpecies