Complexity of triangular representations of algebraic sets

Eli Amzallag; Mengxiao Sun; Gleb Pogudin; Thieu N. Vo

doi:10.1016/j.jalgebra.2019.01.007

Complexity of triangular representations of algebraic sets

Eli Amzallag, Mengxiao Sun, Gleb Pogudin, Thieu N. Vo

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szántó. In this paper, we give the first complete bounds for the degrees of the polynomials and the number of components in the output of the algorithm, providing explicit formulas for these bounds.

Original language	English
Pages (from-to)	342-364
Number of pages	23
Journal	Journal of Algebra
Volume	523
DOIs	https://doi.org/10.1016/j.jalgebra.2019.01.007
Publication status	Published - 1 Apr 2019

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2019.01.007

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title = "Complexity of triangular representations of algebraic sets",

abstract = "Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Sz{\'a}nt{\'o}. In this paper, we give the first complete bounds for the degrees of the polynomials and the number of components in the output of the algorithm, providing explicit formulas for these bounds.",

author = "Eli Amzallag and Mengxiao Sun and Gleb Pogudin and Vo, \{Thieu N.\}",

year = "2019",

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AU - Amzallag, Eli

AU - Sun, Mengxiao

AU - Pogudin, Gleb

AU - Vo, Thieu N.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szántó. In this paper, we give the first complete bounds for the degrees of the polynomials and the number of components in the output of the algorithm, providing explicit formulas for these bounds.

AB - Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szántó. In this paper, we give the first complete bounds for the degrees of the polynomials and the number of components in the output of the algorithm, providing explicit formulas for these bounds.

UR - https://www.scopus.com/pages/publications/85060341128

U2 - 10.1016/j.jalgebra.2019.01.007

DO - 10.1016/j.jalgebra.2019.01.007

M3 - Article

AN - SCOPUS:85060341128

SN - 0021-8693

VL - 523

SP - 342

EP - 364

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Complexity of triangular representations of algebraic sets

Abstract

ASJC Scopus subject areas

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