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).

EXAMPLES:

sage: from sage.categories.additive_monoids import AdditiveMonoids
sage: C.super_categories()
sage: sorted(C.axioms())
True


TESTS:

sage: C.Algebras(QQ).is_subcategory(AlgebrasWithBasis(QQ))
True
sage: TestSuite(C).run()


class ParentMethods
sum(args)

Return the sum of the elements in args, as an element of self.

INPUT:

• args – a list (or iterable) of elements of self

EXAMPLES:

sage: S = CommutativeAdditiveMonoids().example()
sage: S.sum((a,b,a,c,a,b))
3*a + c + 2*b
sage: S.sum(())
0
sage: S.sum(()).parent() == S
True