Notes on triangular sets and triangulation-decomposition algorithms I: polynomial systems

Authors:
Evelyne Hubert
Affiliations:
INRIA - Projet CAFE, Sophia Antipolis
Venue:
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Year:
2001

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Abstract

This is the first in a series of two tutorial articles devoted to triangulation-decomposition algorithms. The value of these notes resides in the uniform presentation of triangulation-decomposition of polynomial and differential radical ideals with detailed proofs of all the presented results. We emphasize the study of the mathematical objects manipulated by the algorithms and show their properties independently of those. We also detail a selection of algorithms, one for each task. We address here polynomial systems and some of the material we develop here will be used in the second part, devoted to differential systems.