Tate introduced in [Ta71] the notion of Tate algebras to serve, in the context of analytic geometry over the-adics, as a counterpart of polynomial algebras in classical algebraic geometry. In [CVV19, CVV20] the formalism of Gr{\"o}bner bases over Tate algebras has been introduced and advanced signature-based algorithms have been proposed. In the present article, we extend the FGLM algorithm of [FGLM93] to Tate algebras. Beyond allowing for fast change of ordering, this strategy has two other important benefits. First, it provides an efficient algorithm for changing the radii of convergence which, in particular, makes effective the bridge between the polynomial setting and the Tate setting and may help in speeding up the computation of Gr{\"o}bner basis over Tate algebras. Second, it gives the foundations for designing a fast algorithm for interreduction, which could serve as basic primitive in our previous algorithms and accelerate them significantly.

中文翻译：

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Tate代数的FGLM算法

泰特（Tate）在[Ta71]中引入了泰特代数的概念，以在addic上的解析几何学中作为经典代数几何中多项式代数的对应物。在[CVV19，CVV20]中，介绍了Tate代数上Gr {\“ o} bner基的形式，并提出了基于签名的高级算法。在本文中，我们将[FGLM93]的FGLM算法扩展到Tate代数除了允许快速改变顺序外，该策略还有另外两个重要优点：首先，它提供了一种有效的算法来改变收敛半径，尤其是有效地建立了多项式设置和Tate设置之间的桥梁，并且可能会有所帮助加快了泰特代数的Gr {b} bner基的计算速度。第二，