  Introduced by Tate in [Ta71], Tate algebras play a major role in the context
of analytic geometry over the-adics, where they act as a counterpart to the use
of polynomial algebras in classical algebraic geometry. In [CVV19] the
formalism of Gr{\"o}bner bases over Tate algebras has been introduced and
effectively implemented. One of the bottleneck in the algorithms was the time
spent on reduction , which are significantly costlier than over polynomials. In
the present article, we introduce two signature-based Gr{\"o}bner bases
algorithms for Tate algebras, in order to avoid many reductions. They have been
implemented in SageMath. We discuss their superiority based on numerical
evidences.
