This command computes the affine hull for the given polyhedral set polyset, returning the result as a new PolyhedralSet.

The affine hull of a line segment is the whole line and that of a 2-D face in a 3-D space is the plane containing the face.

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

$\mathrm{ps1}≔\mathrm{PolyhedralSet}\left(\left[\left[1\,0\,0\right]\,\left[0\,1\,0\right]\,\left[0\,0\,1\right]\right]\right)$

$\mathrm{ps1}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[-x_3\le 0\,-x_2\le 0\,x_2+x_3\le 1\,x_1+x_2+x_3=1\right]\end{array}$

$\mathrm{aff\_ps1}≔\mathrm{AffineHull}\left(\mathrm{ps1}\right)$

$\mathrm{aff\_ps1}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x_1\,x_2\,x_3\right]\\ \mathrm{Relations}& \:& \left[x_1+x_2+x_3=1\right]\end{array}$

$\mathrm{Plot}\left(\left[\mathrm{ps1}\,\mathrm{aff\_ps1}\right]\right)$

$\mathrm{ps2}≔\mathrm{PolyhedralSet}\left(\left[1\le 0\right]\,\left[x\right]\right)\:$$\mathrm{aff\_ps2}≔\mathrm{AffineHull}\left(\mathrm{ps2}\right)$

$\mathrm{aff\_ps2}≔\{\begin{array}{lll}\mathrm{Coordinates}& \:& \left[x\right]\\ \mathrm{Relations}& \:& \left[0\le \mathrm{-1}\right]\end{array}$

$\mathrm{IsEmpty}\left(\mathrm{ps2}\right)$

$\mathrm{true}$

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

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