Prototyping Symbolic-Numeric Algorithms using Naglink¹

B.J. Dupée     &     J.H. Davenport
Department of Mathematical Sciences
University of Bath
Bath     BA2 7AY      UK
email: {bjd,jhd}@maths.bath.ac.uk

Abstract:

There is a fundamental difficulty with the creation of innovative symbolic-numeric algorithms. Whilst links exist between Computer Algebra Systems, they are basically designed to offer the user extra numerical algorithms in the form of existing Numerical Library routines, rather than providing a generic package.

This presentation will show how new algorithms can be created and tested using the linking package provided by Axiom 2.2, Naglink. We will take, as an example, a package which the authors have created for solving initial value problems of ODEs using Taylor series methods.

We will show how the code from the different paradigms can be separately designed in Aldor (or Axiom) and Fortran or C, and how the linking programs, headers and envelopes can be automatically created using specialist software created by NAG for the link to their Numerical Library. We will also show how the symbolic-numeric process is then controlled using the daemon provided with Axiom 2.2.