Functorial composition species

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

EXAMPLES:

sage: G = species.SimpleGraphSpecies()
sage: c = G.generating_series().coefficients(2)
sage: type(G)
<class 'sage.combinat.species.functorial_composition_species.FunctorialCompositionSpecies_class'>
sage: G == loads(dumps(G))
True
sage: G._check() #False due to isomorphism types not being implemented
False
_cis(series_ring, base_ring)

EXAMPLES:

sage: G = species.SimpleGraphSpecies()
sage: G.cycle_index_series().coefficients(5)
[p[],
 p[1],
 p[1, 1] + p[2],
 4/3*p[1, 1, 1] + 2*p[2, 1] + 2/3*p[3],
 8/3*p[1, 1, 1, 1] + 4*p[2, 1, 1] + 2*p[2, 2] + 4/3*p[3, 1] + p[4]]
_default_structure_class
alias of FunctorialCompositionStructure
_gs(series_ring, base_ring)

EXAMPLES:

sage: G = species.SimpleGraphSpecies()
sage: G.generating_series().coefficients(5)
[1, 1, 1, 4/3, 8/3]
_isotypes(structure_class, s)

There is no known algorithm for efficiently generating the isomorphism types of the functorial composition of two species.

EXAMPLES:

sage: G = species.SimpleGraphSpecies()
sage: G.isotypes([1,2,3]).list()
...
NotImplementedError
_itgs(series_ring, base_ring)

EXAMPLES:

sage: G = species.SimpleGraphSpecies()
sage: G.isotype_generating_series().coefficients(5)
[1, 1, 2, 4, 11]
_structures(structure_class, s)

EXAMPLES:

sage: G = species.SimpleGraphSpecies()
sage: G.structures([1,2,3]).list()
[{},
 {{1, 2}*{3}},
 {{1, 3}*{2}},
 {{2, 3}*{1}},
 {{1, 2}*{3}, {1, 3}*{2}},
 {{1, 2}*{3}, {2, 3}*{1}},
 {{1, 3}*{2}, {2, 3}*{1}},
 {{1, 2}*{3}, {1, 3}*{2}, {2, 3}*{1}}]
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
class sage.combinat.species.functorial_composition_species.FunctorialCompositionStructure(parent, labels, list)

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