Sharp estimates for triangular sets

Xavier Dahan; Éric Schost

doi:10.1145/1005285.1005302

Sharp estimates for triangular sets

Xavier Dahan, Éric Schost

IEHE - Division of Developmental Research in Education Programs

Ecole Polytechnique and CNRS-IN2P3

Research output: Contribution to conference › Paper › peer-review

51 Citations (Scopus)

Abstract

We study the triangular representation of zero-dimensional varieties defined over the rational field (resp. a rational function field). We prove polynomial bounds in terms of intrinsic quantities for the height (resp. degree) of the coefficients of such triangular sets, whereas previous bounds were exponential. We also introduce a rational form of triangular representation, for which our estimates become linear. Experiments show the practical interest of this new representation.

Original language	English
Pages	103-110
Number of pages	8
DOIs	https://doi.org/10.1145/1005285.1005302
Publication status	Published - 2004
Event	ISSAC 2004 - International Symposium on Symbolic and Algebraic Computation - Santander, Spain Duration: 2004 Jul 4 → 2004 Jul 7

Conference

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

Keywords

Intrinsic bounds
Polynomial systems
Triangular sets

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10.1145/1005285.1005302

Cite this

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AB - We study the triangular representation of zero-dimensional varieties defined over the rational field (resp. a rational function field). We prove polynomial bounds in terms of intrinsic quantities for the height (resp. degree) of the coefficients of such triangular sets, whereas previous bounds were exponential. We also introduce a rational form of triangular representation, for which our estimates become linear. Experiments show the practical interest of this new representation.

KW - Intrinsic bounds

KW - Polynomial systems

KW - Triangular sets

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

Y2 - 4 July 2004 through 7 July 2004

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Sharp estimates for triangular sets

Abstract

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Keywords

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