Coverage for local/lib/python2.7/site-packages/sage/categories/commutative_algebras.py : 20%

r""" 

Commutative algebras 

""" 

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

# Copyright (C) 2005 David Kohel <kohel@maths.usyd.edu> 

# William Stein <wstein@math.ucsd.edu> 

# 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_over_base_ring 

from sage.categories.algebras import Algebras 

class CommutativeAlgebras(CategoryWithAxiom_over_base_ring): 

""" 

The category of commutative algebras with unit over a given base ring. 

EXAMPLES:: 

sage: M = CommutativeAlgebras(GF(19)) 

sage: M 

Category of commutative algebras over Finite Field of size 19 

sage: CommutativeAlgebras(QQ).super_categories() 

[Category of algebras over Rational Field, Category of commutative rings] 

This is just a shortcut for:: 

sage: Algebras(QQ).Commutative() 

Category of commutative algebras over Rational Field 

TESTS:: 

sage: Algebras(QQ).Commutative() is CommutativeAlgebras(QQ) 

True 

sage: TestSuite(CommutativeAlgebras(ZZ)).run() 

Todo: 

- product ( = Cartesian product) 

- coproduct ( = tensor product over base ring) 

""" 

def __contains__(self, A): 

""" 

EXAMPLES:: 

sage: QQ['a'] in CommutativeAlgebras(QQ) 

True 

sage: QQ['a,b'] in CommutativeAlgebras(QQ) 

True 

sage: FreeAlgebra(QQ,2,'a,b') in CommutativeAlgebras(QQ) 

False 

TODO: get rid of this method once all commutative algebras in 

Sage declare themselves in this category 

""" 

return super(CommutativeAlgebras, self).__contains__(A) or \ 

(A in Algebras(self.base_ring()) and hasattr(A, "is_commutative") and A.is_commutative())