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r""" 

Graded Algebras 

""" 

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

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

# 2008-2011 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.graded_modules import GradedModulesCategory 

 

class GradedAlgebras(GradedModulesCategory): 

""" 

The category of graded algebras 

 

EXAMPLES:: 

 

sage: GradedAlgebras(ZZ) 

Category of graded algebras over Integer Ring 

sage: GradedAlgebras(ZZ).super_categories() 

[Category of filtered algebras over Integer Ring, 

Category of graded modules over Integer Ring] 

 

TESTS:: 

 

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

""" 

class ParentMethods: 

def graded_algebra(self): 

""" 

Return the associated graded algebra to ``self``. 

 

Since ``self`` is already graded, this just returns 

``self``. 

 

EXAMPLES:: 

 

sage: m = SymmetricFunctions(QQ).m() 

sage: m.graded_algebra() is m 

True 

""" 

return self 

 

class ElementMethods: 

pass