4 papers
Computational Algebra with Attention: Transformer Oracles for Border Basis Algorithms
Hiroshi Kera, Nico Pelleriti, Yuki Ishihara +2
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gröbner and…
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…
Comprehensive Systems for Primary Decompositions of Parametric Ideals
Yuki Ishihara, Kazuhiro Yokoyama
We present an effective method for computing parametric primary decomposition via comprehensive Gröbner systems. In general, it is very difficult to compute a parametric primary d…
Primary Decomposition of Symmetric Ideals
Yuki Ishihara
We propose an effective method for primary decomposition of symmetric ideals. Let be the -valuables polynomial ring over a field and $\mathfrak{S}_n…