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

r""" 

Commutative additive semigroups 

""" 

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

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

# 

# 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_semigroups import AdditiveSemigroups 

class CommutativeAdditiveSemigroups(CategoryWithAxiom): 

""" 

The category of additive abelian semigroups, i.e. sets with an 

associative and abelian operation +. 

EXAMPLES:: 

sage: C = CommutativeAdditiveSemigroups(); C 

Category of commutative additive semigroups 

sage: C.example() 

An example of a commutative monoid: the free commutative monoid generated by ('a', 'b', 'c', 'd') 

sage: sorted(C.super_categories(), key=str) 

[Category of additive commutative additive magmas, 

Category of additive semigroups] 

sage: sorted(C.axioms()) 

['AdditiveAssociative', 'AdditiveCommutative'] 

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

True 

.. NOTE:: 

This category is currently empty and only serves as a place 

holder to make ``C.example()`` work. 

TESTS:: 

sage: TestSuite(C).run() 

""" 

_base_category_class_and_axiom = (AdditiveSemigroups, "AdditiveCommutative")