Returns true if the polyhedral set ps1 is contained in the interior of the highest dimensional face of ps2, that is if ps1 is a subset of ps2 and the intersections between the facets of ps1 and the facets of ps2 are empty.

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

$\mathrm{c\_big}≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\left[-1..1\,-1..1\,-1..1\right]\right)$

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

$\mathrm{c\_small}≔\mathrm{ExampleSets}:-\mathrm{Cube}\left(\left[-\frac{1}{10}..\frac{1}{10}\,-\frac{1}{10}..\frac{1}{10}\,-\frac{1}{10}..\frac{1}{10}\right]\right)$

$\mathrm{c\_small}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le \frac{1}{10}\,x_3\le \frac{1}{10}\,-x_2\le \frac{1}{10}\,x_2\le \frac{1}{10}\,-x_1\le \frac{1}{10}\,x_1\le \frac{1}{10}\right]\end{array}$

$\mathrm{IsInInterior}\left(\mathrm{c\_small}\,\mathrm{c\_big}\right)$

$\mathrm{true}$

$\mathrm{Plot}\left(\left[\mathrm{c\_big}\,\mathrm{c\_small}\right]\,\mathrm{faceoptions}=\left[\mathrm{transparency}=\left[0.5\,0.\right]\right]\right)$

$\mathrm{IsInInterior}\left(\mathrm{ExampleSets}:-\mathrm{EmptySet}\left(3\right)\,\mathrm{ExampleSets}:-\mathrm{Cube}\left(\right)\right)$

$\mathrm{false}$

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

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