Coverage for local/lib/python2.7/site-packages/sage/categories/finite_sets.py : 29%

r""" 

Finite sets 

""" 

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

# Copyright (C) 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.category_with_axiom import CategoryWithAxiom 

from sage.categories.algebra_functor import AlgebrasCategory 

from sage.categories.subquotients import SubquotientsCategory 

class FiniteSets(CategoryWithAxiom): 

r""" 

The category of finite sets. 

EXAMPLES:: 

sage: C = FiniteSets(); C 

Category of finite sets 

sage: C.super_categories() 

[Category of sets] 

sage: C.all_super_categories() 

[Category of finite sets, 

Category of sets, 

Category of sets with partial maps, 

Category of objects] 

sage: C.example() 

NotImplemented 

TESTS:: 

sage: TestSuite(C).run() 

sage: C is Sets().Finite() 

True 

""" 

class ParentMethods: 

def is_finite(self): 

""" 

Return ``True`` since ``self`` is finite. 

EXAMPLES:: 

sage: C = FiniteEnumeratedSets().example() 

sage: C.is_finite() 

True 

""" 

return True 

class Subquotients(SubquotientsCategory): 

def extra_super_categories(self): 

r""" 

EXAMPLES:: 

sage: FiniteSets().Subquotients().extra_super_categories() 

[Category of finite sets] 

This implements the fact that a subquotient (and therefore 

a quotient or subobject) of a finite set is finite:: 

sage: FiniteSets().Subquotients().is_subcategory(FiniteSets()) 

True 

sage: FiniteSets().Quotients ().is_subcategory(FiniteSets()) 

True 

sage: FiniteSets().Subobjects ().is_subcategory(FiniteSets()) 

True 

""" 

return [FiniteSets()] 

class Algebras(AlgebrasCategory): 

def extra_super_categories(self): 

r""" 

EXAMPLES:: 

sage: FiniteSets().Algebras(QQ).extra_super_categories() 

[Category of finite dimensional vector spaces with basis over Rational Field] 

This implements the fact that the algebra of a finite set 

is finite dimensional:: 

sage: FiniteMonoids().Algebras(QQ).is_subcategory(AlgebrasWithBasis(QQ).FiniteDimensional()) 

True 

""" 

from sage.categories.modules_with_basis import ModulesWithBasis 

return [ModulesWithBasis(self.base_ring()).FiniteDimensional()]