Sum species

class sage.combinat.species.sum_species.SumSpecies(F, G, min=None, max=None, weight=None)

Bases: sage.combinat.species.species.GenericCombinatorialSpecies, sage.structure.unique_representation.UniqueRepresentation

Returns the sum of two species.

EXAMPLES:

sage: S = species.PermutationSpecies()
sage: A = S+S
sage: A.generating_series().coefficients(5)
[2, 2, 2, 2, 2]

sage: P = species.PermutationSpecies()
sage: F = P + P
sage: F._check()
True
sage: F == loads(dumps(F))
True

TESTS:

sage: A = species.SingletonSpecies() + species.SingletonSpecies()
sage: B = species.SingletonSpecies() + species.SingletonSpecies()
sage: C = species.SingletonSpecies() + species.SingletonSpecies(min=2)
sage: A is B
True
sage: (A is C) or (A == C)
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 add elements of the weight rings for each of the operands.

EXAMPLES:

sage: S = species.SetSpecies()
sage: C = S+S
sage: C.weight_ring()
Rational Field
sage: S = species.SetSpecies(weight=QQ['t'].gen())
sage: C = S + S
sage: C.weight_ring()
Univariate Polynomial Ring in t over Rational Field
class sage.combinat.species.sum_species.SumSpeciesStructure(parent, s, **options)

Bases: sage.combinat.species.structure.SpeciesStructureWrapper

EXAMPLES:

sage: E = species.SetSpecies(); B = E+E
sage: s = B.structures([1,2,3]).random_element()
sage: s.parent()
Sum of (Set species) and (Set species)
sage: s == loads(dumps(s))
True
sage.combinat.species.sum_species.SumSpecies_class

alias of SumSpecies

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