Signature-based algorithms for Gröbner bases over Tate algebras
Language
en
Communication dans un congrès
This item was published in
ISSAC 2021 - International Symposium on Symbolic and Algebraic Computation, 2020-07-20, Kalamata / Virtual.
English Abstract
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] ...Read more >
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.Read less <
English Keywords
F5 algorithm
Gröbner bases
Algorithms
Tate algebra
Power series
P-adic precision
F5 algorithm
Origin
Hal imported