Quelle _Chapter_Attributes_and_properties.xml
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<?xmlversion="1.0"encoding="UTF-8"?>
<!-- This is an automatically generated file. -->
<Chapter Label="Chapter_Attributes_and_properties">
<Heading>Attributes and properties</Heading>
<Section Label="Chapter_Attributes_and_properties_Section_Attributes_and_properties_of_polyhedron">
<Heading>Attributes and properties of polyhedron</Heading>
<ManSection>
<Attr Arg="P" Name="Cdd_Canonicalize" Label="for IsCddPolyhedron"/>
<Returns>a CddPolyhedron
</Returns>
<Description>
The function takes a polyhedron and reduces its defining inequalities (generators set) by deleting all redundant inequalities (generators).
</Description>
</ManSection>
<#Include Label="Example3">
<ManSection>
<Attr Arg="P" Name="Cdd_V_Rep" Label="for IsCddPolyhedron"/>
<Returns>a CddPolyhedron
</Returns>
<Description>
The function takes a polyhedron and returns its reduced <Math>V</Math>-representation.
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_H_Rep" Label="for IsCddPolyhedron"/>
<Returns>a CddPolyhedron
</Returns>
<Description>
The function takes a polyhedron and returns its reduced <Math>H</Math>-representation.
</Description>
</ManSection>
<#Include Label="Example4">
<ManSection>
<Attr Arg="P" Name="Cdd_AmbientSpaceDimension" Label="for IsCddPolyhedron"/>
<Returns>The dimension of the ambient space of the polyhedron(i.e., the space that contains <Math>P</Math>).
</Returns>
<Description>
<P/>
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_Dimension" Label="for IsCddPolyhedron"/>
<Returns>The dimension of the polyhedron, where the dimension, <Math>\mathrm{dim}(P)</Math>, of a polyhedron <Math>P</Math> is the maximum number of affinely independent points in <Math>P</Math> minus 1.
</Returns>
<Description>
<P/>
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_GeneratingVertices" Label="for IsCddPolyhedron"/>
<Returns>The reduced generating vertices of the polyhedron
</Returns>
<Description>
<P/>
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_GeneratingRays" Label="for IsCddPolyhedron"/>
<Returns>list
</Returns>
<Description>
The output is the reduced generating rays of the polyhedron
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_Equalities" Label="for IsCddPolyhedron"/>
<Returns>a list
</Returns>
<Description>
The output is the reduced equalities of the polyhedron.
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_Inequalities" Label="for IsCddPolyhedron"/>
<Description>
The output is the reduced inequalities of the polyhedron.
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_InteriorPoint" Label="for IsCddPolyhedron"/>
<Returns>a list
</Returns>
<Description>
The output is an interior point in the polyhedron
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_Faces" Label="for IsCddPolyhedron"/>
<Returns>a list
</Returns>
<Description>
This function takes a <Math>H</Math>-represented polyhedron <Emph>P</Emph> and returns a list. Every entry in this
list is a again a list, contains the dimension and linearity of the face defined as a polyhedron over the
same system of inequalities.
</Description>
</ManSection>
<ManSection>
<Oper Arg="P, d" Name="Cdd_FacesWithFixedDimension" Label="for IsCddPolyhedron, IsInt"/>
<Returns>a list
</Returns>
<Description>
This function takes a <Math>H</Math>-represented polyhedron <Emph>P</Emph> and a positive integer <Emph>d</Emph>.
The output is a list. Every entry in this
list is the linearity of an <Emph>d</Emph>- dimensional face of <Emph>P</Emph> defined as a polyhedron over the
same system of inequalities.
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_FacesWithInteriorPoints" Label="for IsCddPolyhedron"/>
<Returns>a list
</Returns>
<Description>
This function takes a <Math>H</Math>-represented polyhedron <Emph>P</Emph> and returns a list. Every entry in this
list is a again a list, contains the dimension, linearity of the face defined as a polyhedron over the
same system of inequalities and an interior point in the face.
</Description>
</ManSection>
<ManSection>
<Oper Arg="P, d" Name="Cdd_FacesWithFixedDimensionAndInteriorPoints" Label="for IsCddPolyhedron, IsInt"/>
<Returns>a list
</Returns>
<Description>
This function takes a <Math>H</Math>-represented polyhedron <Emph>P</Emph> and a positive integer <Emph>d</Emph>.
The output is a list. Every entry in this
list is a again a list, contains the linearity of the face defined as a polyhedron over the
same system of inequalities and an interior point in this face.
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_Facets" Label="for IsCddPolyhedron"/>
<Returns>a list
</Returns>
<Description>
This function takes a <Math>H</Math>-represented polyhedron <Emph>P</Emph> and returns a list. Every entry in this
is the linearity of a facet defined as a polyhedron over the
same system of inequalities.
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_Lines" Label="for IsCddPolyhedron"/>
<Returns>a list
</Returns>
<Description>
This function takes a <Math>H</Math>-represented polyhedron <Emph>P</Emph> and returns a list. Every entry in this
is the linearity of a ray (<Math>1</Math>-dimensional face) defined as a polyhedron over the
same system of inequalities.
</Description>
</ManSection>
<ManSection>
<Attr Arg="P" Name="Cdd_Vertices" Label="for IsCddPolyhedron"/>
<Returns>a list
</Returns>
<Description>
This function takes a <Math>H</Math>-represented polyhedron <Emph>P</Emph> and returns a list. Every entry in this
list is the linearity of a vertex defined as a polyhedron over the same system of inequalities.
</Description>
</ManSection>
<ManSection>
<Prop Arg="P" Name="Cdd_IsEmpty" Label="for IsCddPolyhedron"/>
<Returns>true or false
</Returns>
<Description>
The output is <C>true</C> if the polyhedron is empty and <C>false</C> otherwise
</Description>
</ManSection>
<ManSection>
<Prop Arg="P" Name="Cdd_IsCone" Label="for IsCddPolyhedron"/>
<Returns>true or false
</Returns>
<Description>
The output is <C>true</C> if the polyhedron is cone and <C>false</C> otherwise
</Description>
</ManSection>
<ManSection>
<Prop Arg="P" Name="Cdd_IsPointed" Label="for IsCddPolyhedron"/>
<Returns>true or false
</Returns>
<Description>
The output is <C>true</C> if the polyhedron is pointed and <C>false</C> otherwise
</Description>
</ManSection>
<#Include Label="demo">
</Section>
</Chapter>
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