48 citations · 62 across the 14 of their papers we have counts for
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Gröbner bases and critical values: The asymptotic combinatorics of determinantal systems
Alin Bostan, Jérémy Berthomieu, Andrew Ferguson +1
We consider ideals involving the maximal minors of a polynomial matrix. For example, those arising in the computation of the critical values of a polynomial restricted to a variety…
New efficient algorithms for computing Gröbner bases of saturation ideals (F4SAT) and colon ideals (Sparse-FGLM-colon)
Jérémy Berthomieu, Christian Eder, Mohab Safey El Din
This paper is concerned with linear algebra based methods for solving exactly polynomial systems through so-called Gröbner bases, which allow one to compute modulo the polynomial i…
Faster change of order algorithm for Gröbner bases under shape and stability assumptions
Jérémy Berthomieu, Vincent Neiger, Mohab Safey El Din
Solving zero-dimensional polynomial systems using Gröbner bases is usually done by, first, computing a Gröbner basis for the degree reverse lexicographic order, and next computing…