Sum species

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

Bases: GenericCombinatorialSpecies, UniqueRepresentation

Return the sum of two species.

EXAMPLES:

Sage

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()                                                            # needs sage.libs.flint
True
sage: F == loads(dumps(F))
True

Python

>>> from sage.all import *
>>> S = species.PermutationSpecies()
>>> A = S+S
>>> A.generating_series()[:Integer(5)]
[2, 2, 2, 2, 2]

>>> P = species.PermutationSpecies()
>>> F = P + P
>>> F._check()                                                            # needs sage.libs.flint
True
>>> F == loads(dumps(F))
True

left_summand()

Return the left summand of this species.

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> P = species.PermutationSpecies()
>>> F = P + P*P
>>> F.left_summand()
Permutation species

right_summand()

Return the right summand of this species.

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> P = species.PermutationSpecies()
>>> F = P + P*P
>>> F.right_summand()
Product of (Permutation species) and (Permutation species)

weight_ring()

Return 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

sage: S = species.SetSpecies()
sage: C = S+S
sage: C.weight_ring()
Rational Field

Python

>>> from sage.all import *
>>> S = species.SetSpecies()
>>> C = S+S
>>> C.weight_ring()
Rational Field

Sage

sage: S = species.SetSpecies(weight=QQ['t'].gen())
sage: C = S + S
sage: C.weight_ring()
Univariate Polynomial Ring in t over Rational Field

Python

>>> from sage.all import *
>>> S = species.SetSpecies(weight=QQ['t'].gen())
>>> C = S + S
>>> C.weight_ring()
Univariate Polynomial Ring in t over Rational Field

class sage.combinat.species.sum_species.SumSpeciesStructure(parent, s, **options)

Bases: SpeciesStructureWrapper

sage.combinat.species.sum_species.SumSpecies_class

alias of SumSpecies