13 citations · 36 across the 19 of their papers we have counts for
20 papers
A Shape Lemma for Ideals of Differential Operators
Manuel Kauers, Christoph Koutschan, Thibaut Verron
We propose a version of the classical shape lemma for zero-dimensional ideals of a commutative multivariate polynomial ring to the noncommutative setting of zero-dimensional ideals…
Universal Analytic Gr{ö}bner Bases and Tropical Geometry
Tristan Vaccon, Thibaut Verron
A universal analytic Gr{ö}bner basis (UAGB) of an ideal of a Tate algebra is a set containing a local Gr{ö}bner basis for all suitable convergence radii. In a previous article, the…
Signature Gröbner bases in free algebras over rings
Clemens Hofstadler, Thibaut Verron
We generalize signature Gröbner bases, previously studied in the free algebra over a field or polynomial rings over a ring, to ideals in the mixed algebra $R[x_1,...,x_k]\langle y_…
Transcendence Certificates for D-finite Functions
Manuel Kauers, Christoph Koutschan, Thibaut Verron
Although in theory we can decide whether a given D-finite function is transcendental, transcendence proofs remain a challenge in practice. Typically, transcendence is certified by…
Short proofs of ideal membership
Clemens Hofstadler, Thibaut Verron
A cofactor representation of an ideal element, that is, a representation in terms of the generators, can be considered as a certificate for ideal membership. Such a representation…
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 the computation of Gröbner bases for matrix-weighted homogeneous systems
Thibaut Verron
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gröbner bases. We present sev…
Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebra
Clemens Hofstadler, Thibaut Verron
Signature-based algorithms have become a standard approach for computing Gröbner bases in commutative polynomial rings. However, so far, it was not clear how to extend this concept…
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 algorithms for Gr{ö}bner bases over Tate algebras
Xavier Caruso, Tristan Vaccon, Thibaut Verron
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…
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…
Gr{ö}bner bases over Tate algebras
Xavier Caruso, Tristan Vaccon, Thibaut Verron
Tate algebras are fundamental objects in the context of analytic geometry over the p-adics. Roughly speaking, they play the same role as polynomial algebras play in classical algeb…
On Affine Tropical F5 Algorithms
Tristan Vaccon, Thibaut Verron, Kazuhiro Yokoyama
Let be a field equipped with a valuation. Tropical varieties over can be defined with a theory of Gr{ö}bner bases taking into account the valuation of .Because of the us…
A Signature-based Algorithm for computing Computing Gröbner Bases over Principal Ideal Domains
Maria Francis, Thibaut Verron
Signature-based algorithms have become a standard approach for Gröbner basis computations for polynomial systems over fields, but how to extend these techniques to coefficients in…
Determinantal sets, singularities and application to optimal control in medical imagery
Bernard Bonnard, Jean-Charles Faugère, Alain Jacquemard +2
Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast b…
On the complexity of computing Gröbner bases for weighted homogeneous systems
Jean-Charles Faugère, Mohab Safey El Din, Thibaut Verron
Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a…
On the Complexity of Computing Gröbner Bases for Quasi-homogeneous Systems
Jean-Charles Faugère, Mohab Safey El Din, Thibaut Verron
Let $\K$ be a field and $(f_1, \ldots, f_n)\subset \K[X_1, \ldots, X_n]$ be a sequence of quasi-homogeneous polynomials of respective weighted degrees w.r.t a…