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

class sage.categories.polyhedra.PolyhedralSets(R)

Bases: sage.categories.category_types.Category_over_base_ring

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.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'>,
 <type 'object'>]
sage: isinstance(P, P.parent().category().element_class)
True
super_categories()

EXAMPLES:

sage: PolyhedralSets(QQ).super_categories()
[Category of magmas, Category of additive magmas]

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