Counting reducible and singular bivariate polynomials

被引：10
|
作者：
von zur Gathen, Joachim [1 ]
机构：
[1] Univ Bonn, BIT, D-53113 Bonn, Germany
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2008年 / 14卷 / 04期
关键词：
Bivariate polynomial; Finite fields; Combinatorics on polynomials; Counting problems;
D O I：
10.1016/j.ffa.2008.05.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Among the bivariate polynomials over a finite field, most are irreducible. We count some classes of special polynomials, namely the reducible ones, those with a square factor, the "relatively irreducible" ones which are irreducible but factor over an extension field, and the singular ones, which have a root at which both partial derivatives vanish. (C) 2008 Published by Elsevier Inc.
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页码：944 / 978
页数：35
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