Computing the Rational Univariate Represenation of a Polynomial System

Roman Pearce

September 15th, 2004.

A rational univariate representation is a triangular form for a
polynomial system particularily well-suited to symbolic solving.
Most notably, the polynomials in this representation have very small
coefficients - often much smaller than in a lexicographic Groebner basis.
Dahan and Schost proved at ISSAC this year that the size of the
integer coefficients of the polynomials in this representation 
is LINEAR (in certain quantities) whereas they are QUADRATIC 
in a lex Groebner basis.
We will discuss the problem of computing this representation without
introducing large numbers, and we will present a modular method.
A preliminary implementation of this method allows Maple to
solve substantially larger polynomial systems.