Composition species

sage.combinat.species.composition_species.CompositionSpecies(*args, **kwds)

Returns the composition of two species.

EXAMPLES:

sage: E = species.SetSpecies()
sage: C = species.CycleSpecies()
sage: S = E(C)
sage: S.generating_series().coefficients(5)
[1, 1, 1, 1, 1]

TESTS:

sage: E(C) is S
True
class sage.combinat.species.composition_species.CompositionSpeciesStructure(parent, labels, pi, f, gs)

Bases: sage.combinat.species.structure.GenericSpeciesStructure

TESTS:

sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: L = E(C)
sage: a = L.structures(['a','b','c']).random_element()
sage: a == loads(dumps(a))
True
change_labels(labels)

EXAMPLES:

sage: p = PermutationGroupElement((2,3))
sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: L = E(C)
sage: S = L.structures(['a','b','c']).list()
sage: a = S[2]; a
F-structure: {{'a', 'c'}, {'b'}}; G-structures: [('a', 'c'), ('b')]
sage: a.change_labels([1,2,3])
F-structure: {{1, 3}, {2}}; G-structures: [(1, 3), (2)]
transport(perm)

EXAMPLES:

sage: p = PermutationGroupElement((2,3))
sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: L = E(C)
sage: S = L.structures(['a','b','c']).list()
sage: a = S[2]; a
F-structure: {{'a', 'c'}, {'b'}}; G-structures: [('a', 'c'), ('b')]
sage: a.transport(p)
F-structure: {{'a', 'b'}, {'c'}}; G-structures: [('a', 'c'), ('b')]
class sage.combinat.species.composition_species.CompositionSpecies_class(F, G, min=None, max=None, weight=None)

Bases: sage.combinat.species.species.GenericCombinatorialSpecies

EXAMPLES:

sage: E = species.SetSpecies(); C = species.CycleSpecies()
sage: L = E(C)
sage: c = L.generating_series().coefficients(3)
sage: L._check() #False due to isomorphism types not being implemented
False
sage: L == loads(dumps(L))
True
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: E = species.SetSpecies(); C = species.CycleSpecies()
sage: L = E(C)
sage: L.weight_ring()
Rational Field

Previous topic

Sum species

Next topic

Functorial composition species

This Page