FRISCO Project Summary

Project Summary

The aim of the FRISCO project is to investigate and develop technologies which can be used to deliver highly efficient, versatile polynomial solvers to industrial users.

There are many problems which arise in industrial situations which can be reduced to systems of polynomials. Although algorithms exist which, in theory, could provide exact solutions to these problems, in practice they are rarely used outside academic circles for the following reasons:

Existing implementations of these algorithms are not efficient enough to tackle large systems.
The environments in which these algorithms are implemented - typically interactive computer algebra systems - cannot be interfaced to existing scientific applications in an effective way.

Nevertheless there is demonstrable, widespread and persisting interest in applying these algorithms in areas ranging from telecommunications to automated manufacturing and robotics. Such interest provides a strong and encouraging indicator of the industrial relevance of this project.

We propose to develop a new framework which will allow users to integrate symbolic algorithms and other scientific software with the same ease that they can incorporate numerical algorithms into their applications via software libraries such as NAG, LAPACK, IMSL, etc. The framework will have three major components, to meet the particular requirements of computer algebra:

Low-level facilities providing efficient runtime support for memory management and arbitrary precision arithmetic.
Tools for implementing new algorithms and interacting with existing ones, which provide interfaces to conventional language environments.
Libraries of special-purpose implementations of algorithms, optimised for efficiency.

Although designed specifically for polynomial solvers, this framework could be used for implementing other kinds of symbolic algorithms. Many of these facilities will be derived from existing state-of-the-art packages, in particular the algebraic library developed during the ESPRIT project PoSSo, while others will be developed during the course of the project as the result of further research.

There are at least two potential channels for utilising FRISCO's results for the benefit of European industry. The first is by incorporating the technology developed by the project into generally available mathematical, scientific and engineering software packages. The total world-wide market for mathematical packages such as AXIOM, Mathematica, Maple, Matlab, and MathCAD is at present worth 80 MECUs per year, and is said to be growing at around 20% annually. There are already thousands of copies of these packages in use throughout European industry. The second channel is by embedding FRISCO results directly in end user applications. This task may be undertaken by users themselves or through consultancy or value-adding developers.

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