6 citations · 13 across the 16 of their papers we have counts for
16 papers
Gr{ö}bner bases over polytopal affinoid algebras
Moulay A. Barkatou, Lucas Legrand, Tristan Vaccon
Polyhedral affinoid algebras have been introduced by Einsiedler, Kapranov and Lind to connect rigid analytic geometry (analytic geometry over non-archimedean fields) and tropical g…
Hypergeometric Solutions of Linear Difference Systems
Moulay Barkatou, Mark van Hoeij, Johannes Middeke +1
We extend Petkovšek's algorithm for computing hypergeometric solutions of scalar difference equations to the case of difference systems , with ,…
Turrittin's Theorem revisited. The real case
Moulay Barkatou, Félix Álvaro Carnicero-Martín, Fernando Sanz Sánchez
We establish a real version of Turrittin's result on polynomial and formal normal forms of linear systems of ODEs with meromorphic coefficients. Both the normal forms or the transf…
Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory
Primitivo Acosta-Humánez, Moulay Barkatou, Raquel Sánchez-Cauce +1
Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprising…
A Family of Denominator Bounds for First Order Linear Recurrence Systems
Mark van Hoeij, Moulay Barkatou, Johannes Middeke
For linear recurrence systems, the problem of finding rational solutions is reduced to the problem of computing polynomial solutions by computing a content bound or a denominator b…
Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz
Moulay Barkatou, Thomas Cluzeau, Lucia Di Vizio +1
Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504-1516], we prove that a linear differential system is in reduc…