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

r""" 

Polyhedral subsets of free ZZ, QQ or RR-modules. 

""" 

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

# Copyright (C) 2011 Volker Braun <vbraun.name@gmail.com> 

# 

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

# http://www.gnu.org/licenses/ 

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

from sage.misc.cachefunc import cached_method 

from sage.categories.category_types import Category_over_base_ring 

class PolyhedralSets(Category_over_base_ring): 

r""" 

The category of polyhedra over a ring. 

EXAMPLES: 

We create the category of polyhedra over `\QQ`:: 

sage: PolyhedralSets(QQ) 

Category of polyhedral sets over Rational Field 

TESTS:: 

sage: TestSuite(PolyhedralSets(RDF)).run() 

sage: P = Polyhedron() 

sage: P.parent().category().element_class 

<class 'sage.categories.polyhedra.PolyhedralSets.element_class'> 

sage: P.parent().category().element_class.mro() 

[<class 'sage.categories.polyhedra.PolyhedralSets.element_class'>, 

<class 'sage.categories.magmas.Magmas.Commutative.element_class'>, 

<class 'sage.categories.magmas.Magmas.element_class'>, 

<class 'sage.categories.additive_monoids.AdditiveMonoids.element_class'>, 

<class 'sage.categories.additive_magmas.AdditiveMagmas.AdditiveUnital.element_class'>, 

<class 'sage.categories.additive_semigroups.AdditiveSemigroups.element_class'>, 

<class 'sage.categories.additive_magmas.AdditiveMagmas.element_class'>, 

<class 'sage.categories.sets_cat.Sets.element_class'>, 

<class 'sage.categories.sets_with_partial_maps.SetsWithPartialMaps.element_class'>, 

<class 'sage.categories.objects.Objects.element_class'>, 

<... 'object'>] 

sage: isinstance(P, P.parent().category().element_class) 

True 

""" 

def __init__(self, R): 

""" 

TESTS:: 

sage: PolyhedralSets(AA) 

Category of polyhedral sets over Algebraic Real Field 

""" 

Category_over_base_ring.__init__(self, R) 

@cached_method 

def super_categories(self): 

""" 

EXAMPLES:: 

sage: PolyhedralSets(QQ).super_categories() 

[Category of commutative magmas, Category of additive monoids] 

""" 

from sage.categories.magmas import Magmas 

from sage.categories.additive_monoids import AdditiveMonoids 

return [Magmas().Commutative(), AdditiveMonoids()]