We present an algorithm that, given an irreducible polynomial g over a general valued field (K, v), finds the factorization of g over the Henselianization of K under certain conditions. The analysis leading to the algorithm follows the footsteps of Ore, Mac Lane, Okutsu, Montes, Vaquié and Herrera–Olalla–Mahboub–Spivakovsky, whose work we review in our context. The correctness is based on a key new result (Theorem 4.10), exhibiting relations between generalized Newton polygons and factorization in the context of an arbitrary valuation. This allows us to develop a polynomial factorization algorithm and an irreducibility test that go beyond the classical discrete, rank-one case. These foundational results may find applications for various computational tasks involved in arithmetic of function fields, desingularization of hypersurfaces, multivariate Puiseux series or valuation theory.

我们提出了一种算法，给定通用值域 ( K ,  v ) 上的不可约多项式g ，在某些条件下找到g在K的亨森化上的因式分解。该算法的分析遵循了 Ore、Mac Lane、Okutsu、Montes、Vaquié 和 Herrera–Olalla–Mahboub–Spivakovsky 的脚步，我们在本文中回顾了他们的工作。正确性基于一个关键的新结果（定理 4.10），展示了任意评估背景下广义牛顿多边形和因式分解之间的关系。这使我们能够开发超越经典离散、秩一情况的多项式分解算法和不可约性测试。这些基础结果可能会应用于函数域算术、超曲面去奇异化、多元 Puiseux 级数或估值理论等各种计算任务。