apply a linear transformation to a polyhedral set
LinearTransformation(polyset, M, options)
PolyhedralSet to be transformed
matrix with rational entries whose size matches the number of coordinates in polyset
options for setting the transform type and the new coordinates of the transformed set; see the Description Section for details
The LinearTransformation command applies a transformation to the polyhedral set polyset.
When transformtype = forward (default), the transformation y=M⁢x 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=M⁢y 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.
A linear transformation using a matrix with determinant of 2 in 2-D will double the volume of the set.
P ≔ PolyhedralSet⁡0,0,2,3,2,2,x,y:Volume⁡P
M ≔ Matrix⁡2,2,2,3:LinearAlgebra:-Determinant⁡M
T ≔ LinearTransformation⁡P,M:Volume⁡T
The opposite transformation can be applied to get back to the original set
P_again ≔ LinearTransformation⁡T,M,transformtype=inverse:
The PolyhedralSets[LinearTransformation] command was introduced in Maple 2015.
For more information on Maple 2015 changes, see Updates in Maple 2015.
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