LinearitySpace - Maple Help

PolyhedralSets

 LinearitySpace
 linearity space of a polyhedral set

 Calling Sequence LinearitySpace(polyset)

Parameters

 polyset -

Description

 • This command computes the linearity space for the given PolyhedralSet polyset, returning the result as a new PolyhedralSet.
 • The linearity space of a polyhedral set $P$ is defined as the set

$\mathrm{linspace}\left(P\right)≔\left\{z|x+\mathrm{\alpha }\cdot z\in P,\forall x\in P\mathbf{and}\forall \mathrm{\alpha }\in ℝ\right\}$

 which is the largest vector space contained in $P$.

Examples

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

The linearity space of the cube is the origin

 > $c≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right):$$\mathrm{LinearitySpace}\left(c\right)$
 ${{}\begin{array}{lll}{\mathrm{Coordinates}}& {:}& \left[{{x}}_{{1}}{,}{{x}}_{{2}}{,}{{x}}_{{3}}\right]\\ {\mathrm{Relations}}& {:}& \left[{{x}}_{{3}}{=}{0}{,}{{x}}_{{2}}{=}{0}{,}{{x}}_{{1}}{=}{0}\right]\end{array}$ (1)

Compatibility

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