The category of additive monoids.
An additive monoid is a unital class:\(additive semigroup <sage.categories.additive_semigroups.AdditiveSemigroups>\), that is a set endowed with a binary operation \(+\) which is associative and admits a zero (see Wikipedia article Monoid).
sage: from sage.categories.additive_monoids import AdditiveMonoids sage: C = AdditiveMonoids(); C Category of additive monoids sage: C.super_categories() [Category of additive unital additive magmas, Category of additive semigroups] sage: sorted(C.axioms()) ['AdditiveAssociative', 'AdditiveUnital'] sage: from sage.categories.additive_semigroups import AdditiveSemigroups sage: C is AdditiveSemigroups().AdditiveUnital() True
sage: C.Algebras(QQ).is_subcategory(AlgebrasWithBasis(QQ)) True sage: TestSuite(C).run()
alias of AdditiveGroups
Return the sum of the elements in args, as an element of self.
sage: S = CommutativeAdditiveMonoids().example() sage: (a,b,c,d) = S.additive_semigroup_generators() sage: S.sum((a,b,a,c,a,b)) 3*a + c + 2*b sage: S.sum(()) 0 sage: S.sum(()).parent() == S True