LDA (Linear Difference Algebra)

 
This page is under construction.
 
Following is a table of the main commands of the Maple package LDA.  
 
 

Main commands of LDA

Basic commands:
JanetBasis compute the minimal Janet basis for a linear system of difference equations
ShiftGroebnerBasis compute the minimal Groebner basis for a linear system of difference equations
InvReduce reduce (linear) shift expressions w.r.t. a Janet basis
ShiftTabVar display Janet basis with leading monomials and multiplicative variables
HilbertSeries Hilbert series
ZeroSets return the functions by which the involutive basis algorithm had to divide

 
Commands for special applications:
CompCond compatibility conditions for solvability of an affine system of difference equations
CompCondBasis compute the minimal Janet basis for the compatibility conditions of an affine system of difference equations

 
Various invariants derivable from HilbertSeries:
CartanCharacter Cartan characters for a linear system of PDEs
HilbertPolynomial graded Hilbert polynomial
HilbertFunction graded Hilbert function
HP filtered Hilbert polynomial
HF filtered Hilbert function
IndexRegularity index of regularity

 
Translation between differential expressions and shift expressions:
Diff2Shift translate a linear differential expression into a polynomial in the partial differential operators
Shift2Diff translate a polynomial into a linear differential expression

 
Auxiliary commands:
LDAOptions set up options for the current LDA session
LeadingShift return the leading monomial of a given linear shift expression
AssertJanetBasis assure the system that given (lists of) polynomials form a Janet basis
LDAStats display statistical information about the last involutive basis computation

 

 

Download Maple package LDA

 
LDA is available for Maple 9 and Maple 10. (For other Maple versions, please contact the authors.)
 
After downloading the Maple package, you can follow the installation guide below.
 
After installing LDA, it would be helpful if you could send us a short e-mail which explains for what purpose LDA is beneficial for you and which Maple version you use.
 
If you encounter any problem with LDA, don't hesitate to contact us.
 

Installing LDA

 
  1. Copy the LDA library files "LDA.ind", "LDA.lib" for your Maple version (see download) into a directory called "LDA".

  2. Type
     
    libname;
     
    in Maple.

  3. Write
     
    libname := "the global path of the directory LDA", the result of step 2:
     
    For more details, see ?libname in Maple.
     
  4. Try
     
    with(LDA);
     
    If you encounter a 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.

 
If you still have problems concerning the installation of LDA, please contact us.