Quelle _Chapter_Attributes_and_properties.xml Sprache: XML

<?xml version="1.0" encoding="UTF-8"?>


<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>

quality89%

¤ Dauer der Verarbeitung: 0.23 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.