The LinearTransformation command applies a transformation to the polyhedral set polyset.

When transformtype = forward (default), the transformation $y=Mx$ is applied, where $x$ are the set's original coordinates.  The matrix M must be invertible when using this option.

If transformtype = inverse is specified, the transformation $x=My$ is applied, where $x$ are the set's original coordinates.

The names of the new coordinates $y$ can be specified using the coordinates = c option, where c is a list of names.  If not specified, the transformed set's default coordinates have the same name and order as the set's original coordinates.  New coordinate names must be specified when M is not square, i.e. the transformed set has more or fewer coordinates than the original set.

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

$P≔\mathrm{PolyhedralSet}\left(\left[\left[0\,0\right]\,\left[2\,3\right]\,\left[2\,2\right]\right]\,\left[x\,y\right]\right)\:$$\mathrm{Volume}\left(P\right)$

$1$

$M≔\mathrm{Matrix}\left(\left[\left[2\,2\right]\,\left[2\,3\right]\right]\right)\:$$\mathrm{LinearAlgebra}:-\mathrm{Determinant}\left(M\right)$

$2$

$T≔\mathrm{LinearTransformation}\left(P\,M\right)\:$$\mathrm{Volume}\left(T\right)$

$2$

$\mathrm{P\_again}≔\mathrm{LinearTransformation}\left(T\,M\,\mathrm{transformtype}=\mathrm{inverse}\right)\:$

$\mathrm{Volume}\left(\mathrm{P\_again}\right)$

$1$

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

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