Complexity of triangular representations of algebraic sets

JOURNAL OF ALGEBRA

卷:523

Article

Amzallag, Eli^1,2  Sun, Mengxiao²  Pogudin, Gleb^3,5  Vo, Thieu N.⁴ 

[1] CUNY City Coll, Dept Math, New York, NY 10031 USA

[2] CUNY, Grad Ctr, Dept Math, New York, NY 10016 USA

[3] Johannes Kepler Univ Linz, Inst Algebra, A-4040 Linz, Austria

[4] Ton Duc Thang Univ, Fract Calculus Optimizat & Algebra Res Grp, Fac Math & Stat, Ho Chi Minh City, Vietnam

[5] NYU, Courant Inst Math Sci, New York, NY USA

关键词: Triangular set;    Unmixed algebraic set;    Regular chain;    Radical polynomial ideal;    Grobner basis;    Complexity;   

DOI  :  10.1016/j.jalgebra.2019.01.007

来源: Elsevier

【 摘 要 】

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. Szanto. 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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free