PolyhedralSets - Maple Programming Help

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PolyhedralSets

 PolyhedralSet
 construct polyhedral sets

 Calling Sequence PolyhedralSet(system) PolyhedralSet(system, coordinates) PolyhedralSet(vertices, coordinates) PolyhedralSet(vertices, rays, coordinates) PolyhedralSet(polyset)

Parameters

 system - list or set of linear equalities and non-strict inequalities with rational coefficients vertices - list of lists or set of lists of rationals rays - (optional) list/set of list of rationals coordinates - (optional) list of names, coordinates of the set's ambient space polyset - polyhedral set to copy

Description

 • 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

Examples

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

Create a set via a list of inequalities

 > $\mathrm{ps}≔\mathrm{PolyhedralSet}\left(\left[0\le x,0\le y\right]\right)$
 ${\mathrm{ps}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{x}{,}{y}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{y}{\le }{0}{,}{-}{x}{\le }{0}\right]\end{array}$ (1)
 > $\mathrm{Relations}\left(\mathrm{ps}\right)$
 $\left[{-}{y}{\le }{0}{,}{-}{x}{\le }{0}\right]$ (2)
 > $\mathrm{Coordinates}\left(\mathrm{ps}\right)$
 $\left[{x}{,}{y}\right]$ (3)

Specifying the coordinates explicitly controls their order and allows for the inclusion of additional coordinates not appearing in system

 > $\mathrm{ps}≔\mathrm{PolyhedralSet}\left(\left[0\le x,0\le y\right],\left[x,y,z\right]\right)$
 ${\mathrm{ps}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{x}{,}{y}{,}{z}\right]\\ {\mathrm{Relations}}& {:}& \left[{-}{y}{\le }{0}{,}{-}{x}{\le }{0}\right]\end{array}$ (4)
 > $\mathrm{Coordinates}\left(\mathrm{ps}\right)$
 $\left[{x}{,}{y}{,}{z}\right]$ (5)

Create a polyhedral set using its vertices and rays

 > $\mathrm{ps}≔\mathrm{PolyhedralSet}\left(\left[\left[5,-5\right],\left[-5,-5\right]\right],\left[\left[-1,-1\right],\left[1,-1\right]\right]\right)$
 ${\mathrm{ps}}{≔}{{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}\right]\\ {\mathrm{Relations}}& {:}& \left[{{x}}_{{2}}{\le }{-5}{,}{-}{{x}}_{{1}}{+}{{x}}_{{2}}{\le }{0}{,}{{x}}_{{1}}{+}{{x}}_{{2}}{\le }{0}\right]\end{array}$ (6)
 > $\mathrm{Plot}\left(\mathrm{ps}\right)$

Compatibility

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