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()[:5]
[2, 2, 2, 2, 2]

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

left_summand()#

Returns the left summand of this species.

EXAMPLES:

sage: P = species.PermutationSpecies()
sage: F = P + P*P
sage: F.left_summand()
Permutation species

right_summand()#

Returns the right summand of this species.

EXAMPLES:

sage: P = species.PermutationSpecies()
sage: F = P + P*P
sage: F.right_summand()
Product of (Permutation species) and (Permutation species)

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

sage.combinat.species.sum_species.SumSpecies_class#: alias of sage.combinat.species.sum_species.SumSpecies