A universal analytic Gr{\"o}bner basis (UAGB) of an ideal of a Tate algebra is a set containing a local Gr{\"o}bner basis for all suitable convergence radii. In a previous article, the authors proved the existence of finite UAGB's for polynomial ideals, leaving open the question of how to compute them. In this paper, we provide an algorithm computing a UAGB for a given polynomial ideal, by traversing the Gr{\"o}bner fan of the ideal. As an application, it offers a new point of view on algorithms for computing tropical varieties of homogeneous polynomial ideals, which typically rely on lifting the computations to an algebra of power series. Motivated by effective computations in tropical analytic geometry, we also examine local bases for more general convergence conditions, constraining the radii to a convex polyhedron. In this setting, we provide an algorithm to compute local Gr{\"o}bner bases and discuss obstacles towards proving the existence of finite UAGBs. CCS CONCEPTS $\bullet$ Computing methodologies $\rightarrow$ Algebraic algorithms.

翻译：一个泰特代数理想的通用解析格罗布纳基（UAGB）是一个包含所有合适收敛半径下的局部格罗布纳基的集合。在先前的一篇文章中，作者证明了多项式理想的有限UAGB的存在性，但未解决如何计算它们的问题。本文通过遍历理想的格罗布纳扇，提出了一种计算给定多项式理想的UAGB的算法。作为应用，该算法为计算齐次多项式理想的热带簇提供了新视角，而传统的计算方法通常依赖于将计算提升到幂级数代数。受热带解析几何中有效计算的启发，我们还检验了更一般收敛条件下的局部基，将半径约束到凸多面体。在此设定下，我们提出了一种计算局部格罗布纳基的算法，并讨论了证明有限UAGB存在性的障碍。CCS概念：•计算方法→代数算法。