Deterministic genericity for polynomial ideals

被引：15

作者：

Hashemi, Amir ^{[1
,2
]}

Schweinfurter, Michael ^{[3
]}

Seiler, Werner M. ^{[3
]}

机构：

[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, POB 19395-5746, Tehran, Iran

[3] Univ Kassel, Inst Math, D-34132 Kassel, Germany

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2018年 / 86卷

关键词：

Polynomial ideals; Deterministic algorithms; Grobner bases; Pommaret bases; Generic positions; Generic initial ideals; Strongly stable ideals; Stable ideals; Quasi stable ideals; Componentwise stability; beta-maximal position; Noether position; DELTA-REGULARITY; COMBINATORIAL APPROACH; INVOLUTION; MODULES;

D O I：

10.1016/j.jsc.2017.03.008

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent algebraic characterisations are provided. It is shown that in characteristic zero the corresponding generic positions can be obtained with a simple deterministic algorithm. In positive characteristic, only adapted stable positions are reachable except for quasi-stability which is obtainable in any characteristic. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：20 / 50

页数：31

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