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# 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`

  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

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