On the Complexity of Linear Algebra Operations over Algebraic Extension Fields

被引：0
|
作者：
Hashemi, Amir [1 ,2 ]
Lichtblau, Daniel [3 ]
机构：
[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran
[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran 193955746, Iran
[3] Wolfram Res, 100 Trade Ctr Dr, Champaign, IL 61820 USA
来源：
COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, CASC 2023 | 2023年 / 14139卷
关键词：
Gaussian elimination; Minimal polynomial; Polynomial ideals; Grobner bases; FGLM algorithm; Algebraic extension fields; Complexity analysis; GROBNER BASES; POLYNOMIALS;
D O I：
10.1007/978-3-031-41724-5_8
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, we study the complexity of performing some linear algebra operations such as Gaussian elimination and minimal polynomial computation over an algebraic extension field. For this, we use the theory of Grobner bases to employ linear algebra methods as well as to work in an algebraic extension. We show that this has good complexity. Finally, we report an implementation of our algorithms in WOLFRAM MATHEMATICA and illustrate its effectiveness via several examples.
引用
收藏
页码：141 / 161
页数：21
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