Bases: sage.categories.examples.commutative_additive_semigroups.FreeCommutativeAdditiveSemigroup
An example of a commutative additive monoid: the free commutative monoid
This class illustrates a minimal implementation of a commutative monoid.
EXAMPLES:
sage: S = CommutativeAdditiveMonoids().example(); S
An example of a commutative monoid: the free commutative monoid generated by ('a', 'b', 'c', 'd')
sage: S.category()
Category of commutative additive monoids
This is the free semigroup generated by:
sage: S.additive_semigroup_generators()
Family (a, b, c, d)
with product rule given by for all :
sage: (a,b,c,d) = S.additive_semigroup_generators()
We conclude by running systematic tests on this commutative monoid:
sage: TestSuite(S).run(verbose = True)
running ._test_additive_associativity() . . . pass
running ._test_an_element() . . . pass
running ._test_category() . . . pass
running ._test_elements() . . .
Running the test suite of self.an_element()
running ._test_category() . . . pass
running ._test_eq() . . . pass
running ._test_not_implemented_methods() . . . pass
running ._test_pickling() . . . pass
pass
running ._test_elements_eq() . . . pass
running ._test_eq() . . . pass
running ._test_not_implemented_methods() . . . pass
running ._test_pickling() . . . pass
running ._test_some_elements() . . . pass
running ._test_zero() . . . pass
Returns the zero of this additive monoid, as per CommutativeAdditiveMonoids.ParentMethods.zero().
EXAMPLES:
sage: M = CommutativeAdditiveMonoids().example(); M
An example of a commutative monoid: the free commutative monoid generated by ('a', 'b', 'c', 'd')
sage: M.zero()
0