One close experience
FRISCO: A FRamework for Integrated Symbolic/Numeric COmputation (ESPRIT 1996-99)
The Consortium: NAG Ltd (Oxford, UK), U. Cantabria (Spain), U. Pisa (Italy),
U. Rennes I, INRIA Sophia-Antipolis (France)
Questionnaire to Industries + Open Workshop (Barcelona, fall 96):
The Needs of Industry on Polynomial System Solving.
¥Info about the corporation itself
¥How does the polynomial system appear?
¥What kind of system is it (number of variables, coefficient type, etc...)?
¥What kind of solutions are looked for?
¥When has it to be solved (real time, off-line, etc...)?
Info about the corporation itself
Contacted (more than 60):
EDF, Alcatel, FIAT, REIS, Daimler Benz, VW, PEGOP, TECNATOM, CANDEMAT, SIMULOG, CASA, APIA XXI, LABEIN,...
Answered: around a dozen (mostly spanish, also EDF, CCETT, PEGOP, REIS ROBOTICS,etc...)
Attended: about half dozen!!!
The polynomial system
Generated by means of standard Symbolic/Numeric software
Usually same number of equations and of unknowns (from 16 to several thousands)
Quite sparse, but because of presentation
Low degree, two or three
Real numbers, Z_3, exact rational numbers
Parameters are first specialized
¥Real solutions, 10^-7 accuracy, both on or off-line
¥If problems arise (for Newton-like methods) the mathematical model is simplified.
¥Usually, parametric solutions have not been regarded (but it would be wellcome, in principle).