Journal of Symbolic Computation ( IF 0.6 ) Pub Date : 2020-06-17 , DOI: 10.1016/j.jsc.2019.08.005 Jaime Gutierrez , Jorge Jiménez Urroz
One of the fundamental tasks of Symbolic Computation is the factorization of polynomials into irreducible factors. The aim of the paper is to produce new families of irreducible polynomials, generalizing previous results in the area. One example of our general result is that for a near-separated polynomial, i.e., polynomials of the form , then is always irreducible for any constant r different from zero. We also provide the biggest known family of HIP polynomials in several variables. These are polynomials over a zero characteristic field such that is irreducible over for every n-tuple of non constant one variable polynomials over . The results can also be applied to fields of positive characteristic, with some modifications.
中文翻译:
关于某些不可约多项式
符号计算的基本任务之一是将多项式分解为不可约因子。本文的目的是产生新的不可约多项式族,以概括该领域以前的结果。我们的一般结果的一个示例是对于近似分离的多项式,即形式为, 然后 对于任何不为零的常数r总是不可约的。我们还在几个变量中提供了最大的HIP多项式族。这些是多项式 在零特征场上 这样 是不可约的 每n个元组 上的非常数一变量多项式 。经过一些修改,结果也可以应用于具有正特性的领域。