A note on Solving Parametric Polynomial Systems

TL;DR

This paper improves an existing algorithm for solving parametric polynomial systems by ensuring minimal output and eliminating the need to compute ideal radicals, enhancing efficiency and precision.

Contribution

The authors modify Lazard and Rouillier's discriminant variety algorithm to guarantee minimal solutions and remove the radical computation step.

Findings

The improved algorithm produces minimal solution sets.

It avoids the computationally expensive radical of ideals.

The modifications enhance the algorithm's efficiency and accuracy.

Abstract

Lazard and Rouillier in [9], by introducing the concept of discriminant variety, have described a new and efficient algorithm for solving parametric polynomial systems. In this paper we modify this algorithm, and we show that with our improvements the output of our algorithm is always minimal and it does not need to compute the radical of ideals.