 LinearTransformation - Maple Help

PolyhedralSets

 LinearTransformation
 apply a linear transformation to a polyhedral set Calling Sequence LinearTransformation(polyset, M, options) Parameters

 polyset - PolyhedralSet to be transformed M - matrix with rational entries whose size matches the number of coordinates in polyset options - options for setting the transform type and the new coordinates of the transformed set; see the Description Section for details Description

 • 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. Examples

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

A linear transformation using a matrix with determinant of 2 in 2-D will double the volume of the set.

 > $P≔\mathrm{PolyhedralSet}\left(\left[\left[0,0\right],\left[2,3\right],\left[2,2\right]\right],\left[x,y\right]\right):$$\mathrm{Volume}\left(P\right)$
 ${1}$ (1)
 > $M≔\mathrm{Matrix}\left(\left[\left[2,2\right],\left[2,3\right]\right]\right):$$\mathrm{LinearAlgebra}:-\mathrm{Determinant}\left(M\right)$
 ${2}$ (2)
 > $T≔\mathrm{LinearTransformation}\left(P,M\right):$$\mathrm{Volume}\left(T\right)$
 ${2}$ (3)

The opposite transformation can be applied to get back to the original set

 > $\mathrm{P_again}≔\mathrm{LinearTransformation}\left(T,M,\mathrm{transformtype}=\mathrm{inverse}\right):$
 > $\mathrm{Volume}\left(\mathrm{P_again}\right)$
 ${1}$ (4) Compatibility

 • The PolyhedralSets[LinearTransformation] command was introduced in Maple 2015.
 • For more information on Maple 2015 changes, see Updates in Maple 2015.