9 papers
On Polynomial Ideals And Overconvergence In Tate Algebras
Xavier Caruso, Tristan Vaccon, Thibaut Verron
In this paper, we study ideals spanned by polynomials or overconvergent series in a Tate algebra. With state-of-the-art algorithms for computing Tate Gr{ö}bner bases, even if the i…
On FGLM Algorithms with Tate Algebras
Xavier Caruso, Tristan Vaccon, Thibaut Verron
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 g…
On Two Signature Variants Of Buchberger's Algorithm Over Principal Ideal Domains
Maria Francis, Thibaut Verron
Signature-based algorithms have brought large improvements in the performances of Gröbner bases algorithms for polynomial systems over fields. Furthermore, they yield additional da…
The generating function of Kreweras walks with interacting boundaries is not algebraic
Alin Bostan, Manuel Kauers, Thibaut Verron
Beaton, Owczarek and Xu (2019) studied generating functions of Kreweras walks and of reverse Kreweras walks in the quarter plane, with interacting boundaries. They proved that for…
Integral P-Recursive Sequences
Shaoshi Chen, Lixin Du, Manuel Kauers +1
In an earlier paper, the notion of integrality known from algebraic number fields and fields of algebraic functions has been extended to D-finite functions. The aim of the present…
Signature-based Möller's algorithm for strong Gröbner bases over PIDs
Maria Francis, Thibaut Verron
Signature-based algorithms are the latest and most efficient approach as of today to compute Gröbner bases for polynomial systems over fields. Recently, possible extensions of thes…