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Extended Hilbert Irreducibility and Its Applications

✍ Scribed by Ming-Deh Huang; Yiu-Chung Wong

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 175 KB
Volume: 37
Category: Article
ISSN: 0196-6774
DOI: 10.1006/jagm.2000.1098

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✦ Synopsis

We extend the effective Hilbert Irreducibility Theorem concerning the reduction of a single multivariate polynomial to one concerning the reduction of an algebraic set, defined by a system of polynomials.The theorem provides the basis for efficient MonteXarlo computations ' on several problems related to an algebraic set. These include: determining its dimension, counting its components, .checking radical ideal membership and equality of algebraic sets, computing the degree of a component, sampling points in a component, and finding a representative general point for each component.

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