Polyhedral subsets of free ZZ, QQ or RR-modules.¶
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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.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'>, <type 'object'>] sage: isinstance(P, P.parent().category().element_class) True
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super_categories
()¶ EXAMPLES:
sage: PolyhedralSets(QQ).super_categories() [Category of commutative magmas, Category of additive monoids]
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