Functorial composition species

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

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

sage.combinat.species.functorial_composition_species.FunctorialCompositionSpecies_class

alias of FunctorialCompositionSpecies

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