Abstract

We present results on testing the computation of bounds for polynomial divisors and give estimates for their heights. There are also given results on the irreducibility of polynomials and some methods for constructing irreducible polynomials. They are based on properties of Newton’s polygon. Finally we give applications to the irreducibility of univariate polynomials

$$F(X) = \sum\limits_{i = 0}^d \,{{a}_{i}}{{X}^{{d - i}}}$$

over a discrete valuation domain. We give applications to bivariate polynomials.

中文翻译：

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不可约多项式的计算方面

摘要

我们提出了测试多项式除数的边界的结果，并给出了其高度的估计值。也给出了多项式的不可约性的结果以及构造不可约多项式的一些方法。它们基于牛顿多边形的属性。最后，我们将应用应用于一元多项式的不可约性

$$ F（X）= \ sum \ limits_ {i = 0} ^ d \，{{a} _ {i}} {{X} ^ {{d-i}}} $$

在离散的评估域上。我们将应用程序应用于二元多项式。