An Efficient Method to Compute the Univariate Rational
Representation for Zero-Dimensional Systems
Date: July 19th (Friday)
Time: 10:30-11:00
Abstract
Computation of Gröbner basis with respect to lexicographic
order is one of useful methods for computing zeros of a zero-dimensional
ideal numerically, but it is often practically hard because of
swells of intermediate coefficients and results itself.
On the other hand, RUR (Rational Univariate Representation --
formerly known as GSL) represents results as rational expressions
instead of polynomials, and it is empirically known that the
coefficients of the results are very small compared with those of
Gröbner basis elements. RUR was proposed by M.-E. Alonso et al.,
and methods of RUR computation using symmetric function were presented
by F. Rouillier, L. Gonzalez-Vega and G. Trujillo. Here we propose
another method, where main tools are modular Gröbner bases, linear
algebra and Hensel lifting. The method is a modification of our
modular change-of-ordering algorithm for Gröbner basis computation,
and it is easily parallelized.
In this talk, we will present our method, discuss its efficiency and
application to prime decomposition of zero-dimensional radical ideals.
