4 papers
On semidefinite-representable sets over valued fields
Corentin Cornou, Simone Naldi, Tristan Vaccon
Polyhedra and spectrahedra over the real numbers, or more generally their images under linear maps, are respectively the feasible sets of linear and semidefinite programming, and f…
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…
Geometric Generality of Transformer-Based Gröbner Basis Computation
Yuta Kambe, Yota Maeda, Tristan Vaccon
The intersection of deep learning and symbolic mathematics has seen rapid progress in recent years, exemplified by the work of Lample and Charton. They demonstrated that effective…
Learning to Compute Gröbner Bases
Hiroshi Kera, Yuki Ishihara, Yuta Kambe +2
Solving a polynomial system, or computing an associated Gröbner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exp…