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A Sparse Effective Nullstellensatz

✍ Scribed by Martı́n Sombra

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
182 KB
Volume
22
Category
Article
ISSN
0196-8858

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✦ Synopsis

We present bounds for the sparseness in the Nullstellensatz. These bounds can give a much sharper characterization than degree bounds of the monomial structure of the polynomials in the Nullstellensatz in case that the input system is sparse. As a consequence we derive a degree bound which can substantially improve the known ones in case of a sparse system.

In addition we introduce the notion of algebraic degree associated to a polynomial system of equations. We obtain a new degree bound which is sharper than the known ones when this parameter is small. We also improve the previous effective Nullstellensatze in case the input polynomials are quadratic. Öur approach is completely algebraic, and the obtained results are independent of the characteristic of the base field.

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