A modular method to compute the rational univariate representation of zero-dimensional ideals

To give an efficiently computable representation of the zeros of a zero-dim ensional ideal I, Rouillier (1996) introduced the rational univariate repre sentation (RUR) as an extension of the generalized shape lemma (GSL) propos ed by Alonso et al. (1996). In this paper, we propose a new method to compu te the RUR of the radical of I, and report on its practical implementation. In the new method, the RUR of the radical of I is computed efficiently by applying modular techniques to solving the systems of linear equations. The performance of the method is examined by practical experiments. We also di scuss its theoretical efficiency. (C) 1999 Academic Press.