CharacteristicCone - Maple Help

PolyhedralSets

 CharacteristicCone
 characteristic cone of a polyhedral set

 Calling Sequence CharacteristicCone(polyset)

Parameters

 polyset - polyhedral set

Description

 • This command computes the characteristic cone of the polyhedral set polyset, returning the result as a new PolyhedralSet.

Examples

 > $\mathrm{with}\left(\mathrm{PolyhedralSets}\right):$

The characteristic cone for a bounded set is the origin since it has no rays.

 > $c≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\left[x,y,z\right]\right):$$\mathrm{c_cone}≔\mathrm{CharacteristicCone}\left(c\right)$
 ${\mathrm{c_cone}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{x}{,}{y}{,}{z}\right]\\ {\mathrm{Relations}}& {:}& \left[{z}{=}{0}{,}{y}{=}{0}{,}{x}{=}{0}\right]\end{array}$ (1)

The V-Representation of a set and its characteristic cone always have the same rays.

 > $\mathrm{ps}≔\mathrm{PolyhedralSet}\left(\left[10\le x+y\right]\right):$$\mathrm{ps_verts},\mathrm{ps_rays}≔\mathrm{VerticesAndRays}\left(\mathrm{ps}\right):$$\mathrm{ps_rays}$
 $\left[\left[{1}{,}{-1}\right]{,}\left[{-1}{,}{1}\right]{,}\left[{1}{,}{1}\right]\right]$ (2)
 > $\mathrm{ps_cone}≔\mathrm{CharacteristicCone}\left(\mathrm{ps}\right):$$\mathrm{ps_cone_verts},\mathrm{ps_cone_rays}≔\mathrm{VerticesAndRays}\left(\mathrm{ps_cone}\right):$$\mathrm{ps_cone_rays}$
 $\left[\left[{1}{,}{-1}\right]{,}\left[{-1}{,}{1}\right]{,}\left[{1}{,}{1}\right]\right]$ (3)
 > $\mathrm{evalb}\left(\mathrm{ps_rays}=\mathrm{ps_cone_rays}\right)$
 ${\mathrm{true}}$ (4)

Compatibility

 • The PolyhedralSets[CharacteristicCone] command was introduced in Maple 2015.