Main commands of OreMorphisms

 
Following is a table of the main commands of the Maple package OreMorphisms. The suffix, "ConstCoeff" (resp., "Rat") distinguishes the procedures which deal with constant (resp., rational) coefficients from those dealing with polynomial coefficients (no suffix means that the procedures handle the polynomial coefficients case). In this table, A denotes an Ore algebra handled in the Maple package Ore_algebra and M (resp. M') a left A-module finitely presented by a matrix R (resp. R').  
 
 

Functions for computing A-morphisms between M and M' and idempotent A-endomorphisms of M

Morphisms(ConstCoeff,Rat)

Compute a finite family of matrices which define A-morphisms between M and M'

Idempotents(ConstCoeff,Rat)

Compute a finite family of matrices defining idempotent elements of the A-endomorphism ring of M

IdempotentsMat(ConstCoeff,Rat)

Compute a finite family of idempotent matrices defining idempotent elements of the A-endomorphism ring of M

Riccati(ConstCoeff,Rat)

Find a finite family of solutions of the algebraic Riccati equation considered in CluzeauQuadrat08

Functions for computing kernels, images, cokernels and coimages of an A-morphism between M and M'

KerMorphism(Rat)

Compute a presentation of the kernel of an A-morphism between M and M'

ImMorphism(Rat)

Compute a presentation of the image of an A-morphism between M and M'

CoimMorphism(Rat)

Compute a presentation of the coimage of an A-morphism between M and M'

CokerMorphism(Rat)

Compute a presentation of the cokernel of an A-morphism between M and M'

Functions for testing some properties of an A-morphism between M and M'

TestInj(Rat)

Test whether or not a given A-morphism between M and M' is injective

TestSurj(Rat)

Test whether or not a given A-morphism between M and M' is surjective

TestIso(Rat)

Test whether or not a given A-morphism between M and M' is an A-isomorphism

Functions for reducing and decomposing a linear functional system

HeuristicReduction(Rat)

Compute a reduction of the matrix R. The heuristic part corresponds to the computation of bases of the different free left A-modules

HeuristicDecomposition(Rat)

Compute a decomposition of the matrix R. The heuristic part corresponds to the computation of bases of the different free left A-modules


 
Please, see also the Library of Examples.
 

Download Maple package OreMorphisms

Our package is available for download:

 

OreMorphisms requires the Maple library OreModules.
 
After installing OreMorphisms, it would be helpful if you could send us a short e-mail which explains for what purpose OreMorphisms is beneficial for you.
 
If you encounter any problem with OreMorphisms, do not hesitate to contact us.
 

Installing OreMorphisms

  1. Copy the previous .mla file 

  2. Open it with Maple (Execute march(‘open’, "…./OreMorphisms.mla"))
  3. Type

    with(OreMorphisms);


You must get the list of the functions contained in the package. If you do obtain an error message, then you have probably done something wrong in Step 2.
 
A reasonable way to check your installation is to run one of the example worksheets of the Library of Examples.
 
If you still have problems concerning the installation of OreMorphisms, please contact us.