Parents for Polyhedra¶
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sage.geometry.polyhedron.parent.
Polyhedra
(base_ring, ambient_dim, backend=None)¶ Construct a suitable parent class for polyhedra
INPUT:
base_ring
– A ring. Currently there are backends for \(\ZZ\), \(\QQ\), and \(\RDF\).ambient_dim
– integer. The ambient space dimension.backend
– string. The name of the backend for computations. There areseveral backends implemented:
backend="ppl"
uses the Parma Polyhedra Librarybackend="cdd"
uses CDDbackend="normaliz"
uses normalizbackend="polymake"
uses polymakebackend="field"
a generic Sage implementation
OUTPUT:
A parent class for polyhedra over the given base ring if the backend supports it. If not, the parent base ring can be larger (for example, \(\QQ\) instead of \(\ZZ\)). If there is no implementation at all, a
ValueError
is raised.EXAMPLES:
sage: from sage.geometry.polyhedron.parent import Polyhedra sage: Polyhedra(AA, 3) Polyhedra in AA^3 sage: Polyhedra(ZZ, 3) Polyhedra in ZZ^3 sage: type(_) <class 'sage.geometry.polyhedron.parent.Polyhedra_ZZ_ppl_with_category'> sage: Polyhedra(QQ, 3, backend='cdd') Polyhedra in QQ^3 sage: type(_) <class 'sage.geometry.polyhedron.parent.Polyhedra_QQ_cdd_with_category'>
CDD does not support integer polytopes directly:
sage: Polyhedra(ZZ, 3, backend='cdd') Polyhedra in QQ^3
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class
sage.geometry.polyhedron.parent.
Polyhedra_QQ_cdd
(base_ring, ambient_dim, backend)¶ Bases:
sage.geometry.polyhedron.parent.Polyhedra_base
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Element
¶ alias of
Polyhedron_QQ_cdd
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class
sage.geometry.polyhedron.parent.
Polyhedra_QQ_normaliz
(base_ring, ambient_dim, backend)¶ Bases:
sage.geometry.polyhedron.parent.Polyhedra_base
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Element
¶ alias of
Polyhedron_QQ_normaliz
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class
sage.geometry.polyhedron.parent.
Polyhedra_QQ_ppl
(base_ring, ambient_dim, backend)¶ Bases:
sage.geometry.polyhedron.parent.Polyhedra_base
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Element
¶ alias of
Polyhedron_QQ_ppl
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class
sage.geometry.polyhedron.parent.
Polyhedra_RDF_cdd
(base_ring, ambient_dim, backend)¶ Bases:
sage.geometry.polyhedron.parent.Polyhedra_base
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Element
¶ alias of
Polyhedron_RDF_cdd
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class
sage.geometry.polyhedron.parent.
Polyhedra_ZZ_normaliz
(base_ring, ambient_dim, backend)¶ Bases:
sage.geometry.polyhedron.parent.Polyhedra_base
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Element
¶ alias of
Polyhedron_ZZ_normaliz
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class
sage.geometry.polyhedron.parent.
Polyhedra_ZZ_ppl
(base_ring, ambient_dim, backend)¶ Bases:
sage.geometry.polyhedron.parent.Polyhedra_base
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Element
¶ alias of
Polyhedron_ZZ_ppl
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sage.geometry.polyhedron.parent.
Polyhedra_base
¶ Polyhedra in a fixed ambient space.
INPUT:
base_ring
– eitherZZ
,QQ
, orRDF
. The base ring of the ambient module/vector space.ambient_dim
– integer. The ambient space dimension.backend
– string. The name of the backend for computations. There areseveral backends implemented:
backend="ppl"
uses the Parma Polyhedra Librarybackend="cdd"
uses CDDbackend="normaliz"
uses normalizbackend="polymake"
uses polymakebackend="field"
a generic Sage implementation
EXAMPLES:
sage: from sage.geometry.polyhedron.parent import Polyhedra sage: Polyhedra(ZZ, 3) Polyhedra in ZZ^3
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class
sage.geometry.polyhedron.parent.
Polyhedra_field
(base_ring, ambient_dim, backend)¶ Bases:
sage.geometry.polyhedron.parent.Polyhedra_base
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Element
¶ alias of
Polyhedron_field
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class
sage.geometry.polyhedron.parent.
Polyhedra_polymake
(base_ring, ambient_dim, backend)¶ Bases:
sage.geometry.polyhedron.parent.Polyhedra_base
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Element
¶ alias of
Polyhedron_polymake
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