Coverage for local/lib/python2.7/site-packages/sage/categories/super_algebras_with_basis.py : 100%

r""" 

Super algebras with basis 

""" 

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

# Copyright (C) 2015 Travis Scrimshaw <tscrim at ucdavis.edu> 

# 

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

# http://www.gnu.org/licenses/ 

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

from sage.categories.super_modules import SuperModulesCategory 

from sage.categories.algebras import Algebras 

from sage.categories.modules import Modules 

class SuperAlgebrasWithBasis(SuperModulesCategory): 

""" 

The category of super algebras with a distinguished basis 

EXAMPLES:: 

sage: C = Algebras(ZZ).WithBasis().Super(); C 

Category of super algebras with basis over Integer Ring 

TESTS:: 

sage: TestSuite(C).run() 

""" 

def extra_super_categories(self): 

""" 

EXAMPLES:: 

sage: C = Algebras(ZZ).WithBasis().Super() 

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

[Category of graded algebras with basis over Integer Ring, 

Category of super algebras over Integer Ring, 

Category of super modules with basis over Integer Ring] 

""" 

return [self.base_category().Graded()] 

class ParentMethods: 

def graded_algebra(self): 

r""" 

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

See :class:`~sage.algebras.associated_graded.AssociatedGradedAlgebra` 

for the definition and the properties of this. 

.. SEEALSO:: 

:meth:`~sage.categories.filtered_modules_with_basis.ParentMethods.graded_algebra` 

EXAMPLES:: 

sage: W.<x,y> = algebras.DifferentialWeyl(QQ) 

sage: W.graded_algebra() 

Graded Algebra of Differential Weyl algebra of 

polynomials in x, y over Rational Field 

""" 

from sage.algebras.associated_graded import AssociatedGradedAlgebra 

return AssociatedGradedAlgebra(self)