# Sum species¶

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

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
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)

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)
True

sage.combinat.species.sum_species.SumSpecies_class

alias of SumSpecies

Subset Species

Derecated splits