On the number of zeros of multiplicity r

Hans Olav Geil, Casper Thomsen

Research output: Other contributionNet publication - Internet publicationResearch

Abstract

Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of variables and |S|. In the present work we take into account what is the leading monomial. This allows us to consider more general point ensembles and most importantly it allows us to produce much more detailed information about the number of zeros of multiplicity r than can be deduced from the generalized Schwartz-Zippel bound. We present both upper and lower bounds.
Original languageEnglish
Publication date8 Dec 2009
Publication statusPublished - 8 Dec 2009

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Multiplicity
Zero
Multivariate Polynomials
Monomial
Upper and Lower Bounds
Ensemble
Subset
Estimate

Cite this

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abstract = "Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of variables and |S|. In the present work we take into account what is the leading monomial. This allows us to consider more general point ensembles and most importantly it allows us to produce much more detailed information about the number of zeros of multiplicity r than can be deduced from the generalized Schwartz-Zippel bound. We present both upper and lower bounds.",
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On the number of zeros of multiplicity r. / Geil, Hans Olav; Thomsen, Casper.

2009, Article.

Research output: Other contributionNet publication - Internet publicationResearch

TY - ICOMM

T1 - On the number of zeros of multiplicity r

AU - Geil, Hans Olav

AU - Thomsen, Casper

N1 - Senest ændret: 21/12/2009

PY - 2009/12/8

Y1 - 2009/12/8

N2 - Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of variables and |S|. In the present work we take into account what is the leading monomial. This allows us to consider more general point ensembles and most importantly it allows us to produce much more detailed information about the number of zeros of multiplicity r than can be deduced from the generalized Schwartz-Zippel bound. We present both upper and lower bounds.

AB - Let S be a finite subset of a field. For multivariate polynomials the generalized Schwartz-Zippel bound [2], [4] estimates the number of zeros over Sx...xS counted with multiplicity. It does this in terms of the total degree, the number of variables and |S|. In the present work we take into account what is the leading monomial. This allows us to consider more general point ensembles and most importantly it allows us to produce much more detailed information about the number of zeros of multiplicity r than can be deduced from the generalized Schwartz-Zippel bound. We present both upper and lower bounds.

M3 - Net publication - Internet publication

ER -