Functorial composition species¶
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class
sage.combinat.species.functorial_composition_species.
FunctorialCompositionSpecies
(F, G, min=None, max=None, weight=None)¶ Bases:
sage.combinat.species.species.GenericCombinatorialSpecies
Returns the functorial composition of two species.
EXAMPLES:
sage: E = species.SetSpecies() sage: E2 = species.SetSpecies(size=2) sage: WP = species.SubsetSpecies() sage: P2 = E2*E sage: G = WP.functorial_composition(P2) sage: G.isotype_generating_series().coefficients(5) [1, 1, 2, 4, 11] sage: G = species.SimpleGraphSpecies() sage: c = G.generating_series().coefficients(2) sage: type(G) <class 'sage.combinat.species.functorial_composition_species.FunctorialCompositionSpecies'> sage: G == loads(dumps(G)) True sage: G._check() #False due to isomorphism types not being implemented False
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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: G = species.SimpleGraphSpecies() sage: G.weight_ring() Rational Field
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sage.combinat.species.functorial_composition_species.
FunctorialCompositionSpecies_class
¶ alias of
FunctorialCompositionSpecies
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class
sage.combinat.species.functorial_composition_species.
FunctorialCompositionStructure
(parent, labels, list)¶ Bases:
sage.combinat.species.structure.GenericSpeciesStructure
This is a base class from which the classes for the structures inherit.
EXAMPLES:
sage: from sage.combinat.species.structure import GenericSpeciesStructure sage: a = GenericSpeciesStructure(None, [2,3,4], [1,2,3]) sage: a [2, 3, 4] sage: a.parent() is None True sage: a == loads(dumps(a)) True