Functorial composition species

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

Bases: GenericCombinatorialSpecies

Return the functorial composition of two species.

EXAMPLES:

Sage

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()[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

Python

>>> from sage.all import *
>>> E = species.SetSpecies()
>>> 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()

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

sage: G = species.SimpleGraphSpecies()
sage: G.weight_ring()
Rational Field

Python

>>> from sage.all import *
>>> G = species.SimpleGraphSpecies()
>>> G.weight_ring()
Rational Field

sage.combinat.species.functorial_composition_species.FunctorialCompositionSpecies_class

alias of FunctorialCompositionSpecies

class sage.combinat.species.functorial_composition_species.FunctorialCompositionStructure(parent, labels, list)

Bases: GenericSpeciesStructure