The ISOLDE Package

The package ISOLDE (Integration of Systems of Ordinary Linear Differential Equations) written in the computer algebra system Maple V contains functions for the symbolic resolution of systems of ordinary linear differential equations, and more generally linear functional matrix equations


Given a linear differential system of the form 
 
where A is square matrix of dimension n, one can distinguish two types of problems, depending on the form of the coefficients of the matrix A :

  
Local problems : we consider a matrix containing formal meromorphic power series of the form

    

    

    where q is a positive integer and the  are constant matrices over a computable field K. The following functions     are provided for the local analysis of such a system : 


  
    Formal reduction, 
    Exponential parts, 
    Formal solutions. 
  


  
Global problems : the matrix A contains rational     functions.If one consider a point  in the     algebraic closure of K (or the point at infinity), the matrix A has an expansion as meromorphic power series at  . The local analysis at this point give useful information about global (closed form) solutions. The functions are :

      

      
        Rational solutions, 
        Exponential solutions, 
        Rational equivalence, 
        Factorization of completely reducible systems. 
      
  

The package is implemented in the computer algebra system Maple. It contains code written by M.A.Barkatou and E.Pfluegel. Please send questions, comments and bug   reports to us.