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
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
alias of FunctorialCompositionSpecies
Bases: sage.combinat.species.structure.GenericSpeciesStructure
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