A polyhedral set can be created via its H-Representation by calling PolyhedralSet(system).  If the set's coordinates are not supplied, they default to the indeterminates in system.

Alternatively, a polyhedral set can be created via its V-Representation by calling PolyhedralSet(vertices, rays, coordinates), supplying the set's vertices and extreme rays.  The rays are an optional argument, required to represent unbounded sets.  If coordinates is not specified, default coordinates names are generated for the set.

The set is reduced to its minimal representation by removing redundant relations, vertices that can be expressed of convex combinations of the other vertices and rays that are conical combinations of the other rays.  The result is stored in a canonical form and will therefore likely have a different form than that used to create the set.

Polyhedral sets can be copied by calling PolyhedralSet

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

$\mathrm{ps}≔\mathrm{PolyhedralSet}\left(\left[0\le x\,0\le y\right]\right)$

$\mathrm{ps}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x\,y\right]\\ \mathrm{Relations}& \:& \left[-y\le 0\,-x\le 0\right]\end{array}$

$\mathrm{Relations}\left(\mathrm{ps}\right)$

$\left[-y\le 0\,-x\le 0\right]$

$\mathrm{Coordinates}\left(\mathrm{ps}\right)$

$\left[x\,y\right]$

$\mathrm{ps}≔\mathrm{PolyhedralSet}\left(\left[0\le x\,0\le y\right]\,\left[x\,y\,z\right]\right)$

$\mathrm{ps}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x\,y\,z\right]\\ \mathrm{Relations}& \:& \left[-y\le 0\,-x\le 0\right]\end{array}$

$\mathrm{Coordinates}\left(\mathrm{ps}\right)$

$\left[x\,y\,z\right]$

$\mathrm{ps}≔\mathrm{PolyhedralSet}\left(\left[\left[5\,-5\right]\,\left[-5\,-5\right]\right]\,\left[\left[-1\,-1\right]\,\left[1\,-1\right]\right]\right)$

$\mathrm{ps}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\right]\\ \mathrm{Relations}& \:& \left[x_2\le \mathrm{-5}\,-x_1+x_2\le 0\,x_1+x_2\le 0\right]\end{array}$

$\mathrm{Plot}\left(\mathrm{ps}\right)$

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

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