Coverage for local/lib/python2.7/site-packages/sage/categories/commutative_additive_monoids.py : 0%

r""" 

Commutative additive monoids 

""" 

#***************************************************************************** 

# Copyright (C) 2008 Teresa Gomez-Diaz (CNRS) <Teresa.Gomez-Diaz@univ-mlv.fr> 

# 2008-2009 Nicolas M. Thiery <nthiery at users.sf.net> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#****************************************************************************** 

from sage.categories.category_with_axiom import CategoryWithAxiom 

from sage.categories.additive_monoids import AdditiveMonoids 

class CommutativeAdditiveMonoids(CategoryWithAxiom): 

""" 

The category of commutative additive monoids, that is abelian 

additive semigroups with a unit 

EXAMPLES:: 

sage: C = CommutativeAdditiveMonoids(); C 

Category of commutative additive monoids 

sage: C.super_categories() 

[Category of additive monoids, Category of commutative additive semigroups] 

sage: sorted(C.axioms()) 

['AdditiveAssociative', 'AdditiveCommutative', 'AdditiveUnital'] 

sage: C is AdditiveMagmas().AdditiveAssociative().AdditiveCommutative().AdditiveUnital() 

True 

.. NOTE:: 

This category is currently empty and only serves as a place 

holder to make ``C.example()`` work. 

TESTS:: 

sage: TestSuite(CommutativeAdditiveMonoids()).run() 

""" 

_base_category_class_and_axiom = (AdditiveMonoids, "AdditiveCommutative")