Let $(K,v)$ be a valued field, and μ an inductive valuation on $K[x]$ extending v. Let ${\mathcal{G}}_{\mu }$ be the graded algebra of μ over $K[x]$, and κ the maximal subfield of the subring of ${\mathcal{G}}_{\mu }$ formed by the homogeneous elements of degree zero.

In this paper, we find an algorithm to compute the field κ and the residual polynomial operator $R_{\mu }:K[x]\to \kappa [y]$, where y is another indeterminate, without any need to perform computations in the graded algebra.

This leads to an OM algorithm to compute the factorization of separable defectless polynomials over henselian fields.

中文翻译：

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归纳估值的残差多项式运算符的计算

让 $（ķ，v）$是一个有价字段，而μ是对$ķ[X]$扩展v。让${\mathcal{G}}_{\mu }$是分级代数μ超过$ķ[X]$，和κ的子环最大子域${\mathcal{G}}_{\mu }$ 由零度的齐次元素组成。

在本文中，我们找到了一种计算场κ和残差多项式算子的算法${\mathrm{[R}}_{\mu }：ķ[X]\to \kappa [ÿ]$，其中y是另一个不确定的，而无需在渐变代数中执行计算。

这导致了OM算法来计算henselian字段上可分离的无缺陷多项式的因式分解。