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On some classes of irreducible polynomials
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 F(x,y)=f1(x)f2(y)f2(x)f1(y), then F(x,y)+r 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 p(x1,,xn)K[x1,,xn] over a zero characteristic field K such that p(h1(x1),,hn(xn)) is irreducible over K for every n-tuple h1(x1),,hn(xn) of non constant one variable polynomials over K. 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FXÿ=F1个XF2ÿ-F2XF1个ÿ, 然后 FXÿ+[R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pX1个Xñķ[X1个Xñ] 在零特征场上 ķ 这样 pH1个X1个HñXñ 是不可约的 ķn个元组H1个X1个HñXñ 上的非常数一变量多项式 ķ。经过一些修改,结果也可以应用于具有正特性的领域。

更新日期:2020-06-17
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