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.

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

$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)$

$\mathrm{true}$

$c≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right)\:$

$\mathrm{c\_faces}≔\mathrm{Faces}\left(c\right)$

$\mathrm{c\_faces}≔\left[\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 1\,x_3\le 1\,-x_2\le 1\,x_2\le 1\,x_1=\mathrm{-1}\right]\end{array}\,\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 1\,x_3\le 1\,-x_2\le 1\,x_2\le 1\,x_1=1\right]\end{array}\,\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 1\,x_3\le 1\,x_2=\mathrm{-1}\,-x_1\le 1\,x_1\le 1\right]\end{array}\,\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 1\,x_3\le 1\,x_2=1\,-x_1\le 1\,x_1\le 1\right]\end{array}\,\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[x_3=\mathrm{-1}\,-x_2\le 1\,x_2\le 1\,-x_1\le 1\,x_1\le 1\right]\end{array}\,\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[x_3=1\,-x_2\le 1\,x_2\le 1\,-x_1\le 1\,x_1\le 1\right]\end{array}\right]$

$\mathrm{map}\left(\mathrm{IsFace}\,\mathrm{c\_faces}\,c\right)$

$\left[\mathrm{true}\,\mathrm{true}\,\mathrm{true}\,\mathrm{true}\,\mathrm{true}\,\mathrm{true}\right]$

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

For more information on Maple 2015 changes, see Updates in Maple 2015.