1 citations · 2 across the 7 of their papers we have counts for
7 papers
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 expo…
Analysis of computing Gröbner bases and Gröbner degenerations via theory of signatures
Yuta Kambe
The signatures of polynomials were originally introduced by Faugère for the efficient computation of Gröbner bases [Fau02], and redefined by Arri-Perry [AP11] as the standard monom…
The Gröbner fan of the Hilbert scheme
Yuta Kambe, Paolo Lella
We give a notion of "combinatorial proximity" among strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. We show that this notion guarantees "geometri…
Computable Białynicki-Birula decomposition of the Hilbert scheme
Yuta Kambe
We call the scheme parameterizing homogeneous ideals with fixed initial ideal the Gröbner scheme. We introduce a Białynicki-Birula decomposition of the Hilbert scheme $\mathrm{Hilb…
Gröbner scheme in the Hilbert scheme and complete intersection monomial ideals
Yuta Kambe
Let be a commutative ring and be a polynomial ring over with a monomial order. For any monomial ideal , there exists an affine -scheme of fini…
Construction of the moduli space of reduced Groebner bases
Yuta Kambe
For a given monomial ideal and a given monomial order , the moduli functor of all reduced Gröbner bases with respect to whose initial…