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PolyhedralSets

  

LinearTransformation

  

apply a linear transformation to a polyhedral set

 

Calling Sequence

Parameters

Description

Examples

Compatibility

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

withPolyhedralSets:

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

PPolyhedralSet0,0,2,3,2,2,x,y:VolumeP

1

(1)

MMatrix2,2,2,3:LinearAlgebra:-DeterminantM

2

(2)

TLinearTransformationP,M:VolumeT

2

(3)

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

P_againLinearTransformationT,M,transformtype=inverse:

VolumeP_again

1

(4)

Compatibility

• 

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

• 

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

See Also

PolyhedralSets

PolyhedralSets[PolyhedralSet]

PolyhedralSets[Project]

 


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