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

 
OreMorphisms is available for Maple 9.5 and Maple 10:
 
After downloading the Maple package, you can follow the installation guide below.
 
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 file "OreMorphisms.m", which is the library OreMorphisms (see download), into a directory called "OreMorphisms".
  2. Type
     
    libname;
     
    in Maple.
  3. Write
     
    libname := " "the global path of the directory OreMorphisms", the result of step 2:
     
  4. Try
     
    with(OreModules);
    with(OreMorphisms);

     
    If you encounter any problem, then most probably the definition of libname in step 3 is wrong in the sense that its value does not point to the correct directory where your library files reside.
     
    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.