论文标题
基于签名的基于gr {Ö} bner基础的算法在泰特代数上
Signature-based algorithms for Gr{ö}bner bases over Tate algebras
论文作者
论文摘要
TATE代数在[TA71]中引入的，在分析的几何形状的背景下起着重要作用，它们与在经典代数几何学中使用多项式代数的同一性作用。在[CVV19]中，已经引入并有效地实施了泰特代数的gr {Ö}基地的形式主义。算法中的瓶颈之一是在减少上花费的时间，这比多项式上的时间明显更为昂贵。在本文中，我们介绍了两个基于签名的GR {Ö} BNER基础算法的泰特代数，以避免进行多次减少。它们已在Sagemath中实施。我们根据数值证据讨论它们的优势。
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{ö}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{ö}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.
