Conclusions

  From section 5.3, it is clear that the requirements on speed and admissible size varies drastically from one case to another. It is clear at this moment that the resolution of nonlinear systems with thousands of equations and unknowns are far from the capabilities of the FRISCO project but probably, in many cases, FRISCO could help to reformulate the mathematical problem in such a way that the system to solve is much smaller.

The research related to the determination of the specific kind of problems arising from real-world problems that FRISCO will be capable of solving is a very active task inside the project. A first step in this direction has been the consolidation of the initial links with companies, enterprises and R&D laboratories interested on FRISCO capabilities and to look for new contacts. Secondly, some actions inside FRISCO were initiated. For example the following areas have already been identified as cornerstones for the project:

• To make explicit the capabilities of FRISCO when dealing with the resolution of polynomial systems involving parameters: in many cases the companies contacted did not imagine that such a possibility exists and is available for non trivial problems.
• To determine some specific needs in the CAD area with respect to polynomial system solving: a first problem is the development of a complete translator between VDA and IGES formats (CANDEMAT and LABEIN are already interested).
• To create/investigate links between FRISCO software and nonlinear optimization packages, or between FRISCO techniques and the theory of linear systems and control.
• To develop inside FRISCO facilities to deal with the nonlinear systems of equations which are produced by discretization schemes or finite elements.
• To establish a good collection of test suites, not only with a statement of the problem and results, but also containing calling sequences allowing the user to experiment with every system on a WWW server providing access to the FRISCO software. This is already available from http://www.inria.fr/safir/POL/ and http://janet.dm.unipi.it/posso_demo.html.

Another useful conclusion from this report is that, in many cases, the industries and companies contacted are proposing a problem that FRISCO methodology cannot solve. This is probably due to the fact that the modelling performed does not exploit the mathematical model underlying the real problem under consideration. This often appears when the nonlinear system of equations comes from a discretization scheme or from a finite element formulation (as in the APIA XXI case).