Functorial composition species¶
- class sage.combinat.species.functorial_composition_species.FunctorialCompositionSpecies(F, G, min=None, max=None, weight=None)[source]¶
Bases:
GenericCombinatorialSpeciesReturn the functorial composition of two species.
EXAMPLES:
sage: E = species.SetSpecies() doctest:warning... DeprecationWarning: combinat.species is superseded by LazyCombinatorialSpecies See https://github.com/sagemath/sage/issues/38544 for details. 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()[0:5] # needs sage.modules [1, 1, 2, 4, 11] sage: G = species.SimpleGraphSpecies() sage: c = G.generating_series()[0:2] 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 # needs sage.modules False
>>> from sage.all import * >>> E = species.SetSpecies() doctest:warning... DeprecationWarning: combinat.species is superseded by LazyCombinatorialSpecies See https://github.com/sagemath/sage/issues/38544 for details. >>> E2 = species.SetSpecies(size=Integer(2)) >>> WP = species.SubsetSpecies() >>> P2 = E2*E >>> G = WP.functorial_composition(P2) >>> G.isotype_generating_series()[Integer(0):Integer(5)] # needs sage.modules [1, 1, 2, 4, 11] >>> G = species.SimpleGraphSpecies() >>> c = G.generating_series()[Integer(0):Integer(2)] >>> type(G) <class 'sage.combinat.species.functorial_composition_species.FunctorialCompositionSpecies'> >>> G == loads(dumps(G)) True >>> G._check() # False due to isomorphism types not being implemented # needs sage.modules False
- weight_ring()[source]¶
Return 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
>>> from sage.all import * >>> G = species.SimpleGraphSpecies() >>> G.weight_ring() Rational Field
- sage.combinat.species.functorial_composition_species.FunctorialCompositionSpecies_class[source]¶
alias of
FunctorialCompositionSpecies
- class sage.combinat.species.functorial_composition_species.FunctorialCompositionStructure(parent, labels, list)[source]¶
Bases:
GenericSpeciesStructure