On reducing a system of equations to a single equation

Gudmund S. Frandsen; Igor E. Shparlinski

On reducing a system of equations to a single equation

Gudmund S. Frandsen^*, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

Abstract

For a system of polynomial equations over Q_p we present an efficient construction of a single polynomial of quite small degree whose zero set over Q_p coincides with, the zero set over Q_p of the original system. We also show that the polynomial has some other attractive features such as low additive and straight-line complexity. The proof is based on a link established here between the above problem and some recent number theoretic result about zeros of p-adic forms.

Original language	English
Title of host publication	ISSAC 2004 - Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation
Editors	Jaime Gutierrez
Place of Publication	New York
Publisher	Association for Computing Machinery (ACM)
Pages	163-166
Number of pages	4
ISBN (Print)	9781581138276
Publication status	Published - 2004
Event	ISSAC 2004 - International Symposium on Symbolic and Algebraic Computation - Santander, Spain Duration: 4 Jul 2004 → 7 Jul 2004

Other

Other	ISSAC 2004 - International Symposium on Symbolic and Algebraic Computation
Country/Territory	Spain
City	Santander
Period	4/07/04 → 7/07/04

Keywords

System of Equations

Cite this

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title = "On reducing a system of equations to a single equation",

abstract = "For a system of polynomial equations over Qp we present an efficient construction of a single polynomial of quite small degree whose zero set over Qp coincides with, the zero set over Qp of the original system. We also show that the polynomial has some other attractive features such as low additive and straight-line complexity. The proof is based on a link established here between the above problem and some recent number theoretic result about zeros of p-adic forms.",

keywords = "System of Equations",

author = "Frandsen, {Gudmund S.} and Shparlinski, {Igor E.}",

year = "2004",

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editor = "Jaime Gutierrez",

booktitle = "ISSAC 2004 - Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation",

publisher = "Association for Computing Machinery (ACM)",

address = "United States",

note = "ISSAC 2004 - International Symposium on Symbolic and Algebraic Computation ; Conference date: 04-07-2004 Through 07-07-2004",

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Frandsen, GS & Shparlinski, IE 2004, On reducing a system of equations to a single equation. in J Gutierrez (ed.), ISSAC 2004 - Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation. Association for Computing Machinery (ACM), New York, pp. 163-166, ISSAC 2004 - International Symposium on Symbolic and Algebraic Computation, Santander, Spain, 4/07/04.

On reducing a system of equations to a single equation. / Frandsen, Gudmund S.; Shparlinski, Igor E.
ISSAC 2004 - Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation. ed. / Jaime Gutierrez. New York: Association for Computing Machinery (ACM), 2004. p. 163-166.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

TY - GEN

T1 - On reducing a system of equations to a single equation

AU - Frandsen, Gudmund S.

AU - Shparlinski, Igor E.

PY - 2004

Y1 - 2004

N2 - For a system of polynomial equations over Qp we present an efficient construction of a single polynomial of quite small degree whose zero set over Qp coincides with, the zero set over Qp of the original system. We also show that the polynomial has some other attractive features such as low additive and straight-line complexity. The proof is based on a link established here between the above problem and some recent number theoretic result about zeros of p-adic forms.

AB - For a system of polynomial equations over Qp we present an efficient construction of a single polynomial of quite small degree whose zero set over Qp coincides with, the zero set over Qp of the original system. We also show that the polynomial has some other attractive features such as low additive and straight-line complexity. The proof is based on a link established here between the above problem and some recent number theoretic result about zeros of p-adic forms.

KW - System of Equations

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M3 - Conference proceeding contribution

AN - SCOPUS:27644599514

SN - 9781581138276

SP - 163

EP - 166

BT - ISSAC 2004 - Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation

A2 - Gutierrez, Jaime

PB - Association for Computing Machinery (ACM)

CY - New York

T2 - ISSAC 2004 - International Symposium on Symbolic and Algebraic Computation

Y2 - 4 July 2004 through 7 July 2004

ER -

On reducing a system of equations to a single equation

Abstract

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