Signature-based algorithms for Gröbner bases over Tate algebras
Sprache des Titels:
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 Gröbner 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 Gröbner 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.