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 tex2html_wrap_inline22 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 tex2html_wrap_inline28 in the algebraic closure of K (or the point at infinity), the matrix A has an expansion as meromorphic power series at tex2html_wrap_inline28 . 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.