IsFace - Maple Help

PolyhedralSets

 IsFace
 test whether or not a given polyhedral set is a face of another polyhedral set

 Calling Sequence IsFace(ps1, ps2)

Parameters

 ps1 - PolyhedralSet, the potential face of ps2 ps2 - PolyhedralSet, the polyhedral set possibly containing ps1 as a face

Description

 • Checks to see if the $n$ dimensional set ps1 is an $n$-face of the $m$ dimensional set ps2.
 • This command checks for proper faces only, so that the dimension of ps1 must be at least zero (a vertex) and at most $m-1$ (a facet of ps2).  The empty set is not considered a face of ps2.

Examples

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

A vertex is a 0-face of a set

 > $p≔\mathrm{PolyhedralSet}\left(\left[\left[1,0\right],\left[0,1\right],\left[1,1\right],\left[0,0\right]\right],\left[x,y\right]\right):$$\mathrm{p_vertex}≔\mathrm{PolyhedralSet}\left(\left[\left[1,0\right]\right],\left[x,y\right]\right):$$\mathrm{IsFace}\left(\mathrm{p_vertex},p\right)$
 ${\mathrm{true}}$ (1)

The faces of a set will return true when tested using IsFace

 > $c≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right):$
 > $\mathrm{c_faces}≔\mathrm{Faces}\left(c\right)$
 ${\mathrm{c_faces}}{≔}\left[{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{{x}}_{{3}}{\le }{1}{,}{{x}}_{{3}}{\le }{1}{,}{-}{{x}}_{{2}}{\le }{1}{,}{{x}}_{{2}}{\le }{1}{,}{{x}}_{{1}}{=}{-1}\right]\end{array}{,}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{{x}}_{{3}}{\le }{1}{,}{{x}}_{{3}}{\le }{1}{,}{-}{{x}}_{{2}}{\le }{1}{,}{{x}}_{{2}}{\le }{1}{,}{{x}}_{{1}}{=}{1}\right]\end{array}{,}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{{x}}_{{3}}{\le }{1}{,}{{x}}_{{3}}{\le }{1}{,}{{x}}_{{2}}{=}{-1}{,}{-}{{x}}_{{1}}{\le }{1}{,}{{x}}_{{1}}{\le }{1}\right]\end{array}{,}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{{x}}_{{3}}{\le }{1}{,}{{x}}_{{3}}{\le }{1}{,}{{x}}_{{2}}{=}{1}{,}{-}{{x}}_{{1}}{\le }{1}{,}{{x}}_{{1}}{\le }{1}\right]\end{array}{,}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{{x}}_{{3}}{=}{-1}{,}{-}{{x}}_{{2}}{\le }{1}{,}{{x}}_{{2}}{\le }{1}{,}{-}{{x}}_{{1}}{\le }{1}{,}{{x}}_{{1}}{\le }{1}\right]\end{array}{,}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{{x}}_{{3}}{=}{1}{,}{-}{{x}}_{{2}}{\le }{1}{,}{{x}}_{{2}}{\le }{1}{,}{-}{{x}}_{{1}}{\le }{1}{,}{{x}}_{{1}}{\le }{1}\right]\end{array}\right]$ (2)
 > $\mathrm{map}\left(\mathrm{IsFace},\mathrm{c_faces},c\right)$
 $\left[{\mathrm{true}}{,}{\mathrm{true}}{,}{\mathrm{true}}{,}{\mathrm{true}}{,}{\mathrm{true}}{,}{\mathrm{true}}\right]$ (3)

Compatibility

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