Functorial composition species

class sage.combinat.species.functorial_composition_species.FunctorialCompositionSpecies(F, G, min=None, max=None, weight=None)[source]

Bases: GenericCombinatorialSpecies

Return 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DeprecationWarning: combinat.species is superseded by LazyCombinatorialSpecies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DeprecationWarning: combinat.species is superseded by LazyCombinatorialSpecies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