IsEmpty - Maple Help
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PolyhedralSets

 IsEmpty
 check if a polyhedral set is empty
 IsUniversalSet
 check if a polyhedral set is the universal set

Calling Sequence

 IsEmpty(polyset) IsUniversalSet(polyset)

Parameters

 polyset -

Description

 • IsEmpty returns true if the polyhedral set polyset is the empty set, false otherwise.
 • IsUniversalSet returns true if the polyhedral set polyset is the universal set, false otherwise.

Examples

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

Sets specified with infeasible relations are empty.

 > $\mathrm{p_empty}≔\mathrm{PolyhedralSet}\left(\left[1\le x,x\le -1\right]\right):$$\mathrm{IsEmpty}\left(\mathrm{p_empty}\right)$
 ${\mathrm{true}}$ (1)

The convex hull of an inequality and its reversed inequality gives the universal set.

 > $\mathrm{p_left}≔\mathrm{PolyhedralSet}\left(\left[1\le x\right]\right):$$\mathrm{p_right}≔\mathrm{PolyhedralSet}\left(\left[x\le 1\right]\right):$$\mathrm{IsUniversalSet}\left(\mathrm{ConvexHull}\left(\mathrm{p_left},\mathrm{p_right}\right)\right)$
 ${\mathrm{true}}$ (2)

Compatibility

 • The PolyhedralSets[IsEmpty] and PolyhedralSets[IsUniversalSet] commands were introduced in Maple 2015.
 • For more information on Maple 2015 changes, see Updates in Maple 2015.