Sum species¶
- class sage.combinat.species.sum_species.SumSpecies(F, G, min=None, max=None, weight=None)[source]¶
Bases:
GenericCombinatorialSpecies
,UniqueRepresentation
Return 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() # needs sage.libs.flint True sage: F == loads(dumps(F)) True
>>> 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()[source]¶
Return the left summand of this species.
EXAMPLES:
sage: P = species.PermutationSpecies() sage: F = P + P*P sage: F.left_summand() Permutation species
>>> from sage.all import * >>> P = species.PermutationSpecies() >>> F = P + P*P >>> F.left_summand() Permutation species
- right_summand()[source]¶
Return 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)
>>> from sage.all import * >>> P = species.PermutationSpecies() >>> F = P + P*P >>> F.right_summand() Product of (Permutation species) and (Permutation species)
- weight_ring()[source]¶
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: S = species.SetSpecies() sage: C = S+S sage: C.weight_ring() Rational Field
>>> from sage.all import * >>> S = species.SetSpecies() >>> C = S+S >>> 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
>>> 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)[source]¶
Bases:
SpeciesStructureWrapper
- sage.combinat.species.sum_species.SumSpecies_class[source]¶
alias of
SumSpecies