Sharp estimates for triangular sets

Xavier Dahan; Éric Schost

doi:10.1145/1005285.1005302

Sharp estimates for triangular sets

Xavier Dahan, Éric Schost

研究成果: Paper › 査読

49 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ	103-110
ページ数	8
DOI	https://doi.org/10.1145/1005285.1005302
出版ステータス	Published - 2004
外部発表	はい
イベント	ISSAC 2004 - International Symposium on Symbolic and Algebraic Computation - Santander, Spain 継続期間: 2004 7月 4 → 2004 7月 7

Conference

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

ASJC Scopus subject areas

数学 (全般)

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10.1145/1005285.1005302

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引用スタイル

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title = "Sharp estimates for triangular sets",

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.",

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author = "Xavier Dahan and {\'E}ric Schost",

year = "2004",

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AU - Schost, Éric

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N2 - 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.

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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DO - 10.1145/1005285.1005302

M3 - Paper

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

Y2 - 4 July 2004 through 7 July 2004

ER -

Sharp estimates for triangular sets

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Conference

ASJC Scopus subject areas

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