# Faster Change of Order Algorithm for Gröbner Bases under Shape and Stability Assumptions

@article{Berthomieu2022FasterCO, title={Faster Change of Order Algorithm for Gr{\"o}bner Bases under Shape and Stability Assumptions}, author={J{\'e}r{\'e}my Berthomieu and Vincent Neiger and Mohab Safey El Din}, journal={Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation}, year={2022} }

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 the lexicographic Gröbner basis with a change of order algorithm. Currently, the change of order now takes a significant part of the whole solving time for many generic instances. Like the fastest known change of order algorithms, this work focuses on the situation where the ideal defined by the system satisfies…

## 2 Citations

### Finer Complexity Estimates for the Change of Ordering of Gröbner Bases for Generic Symmetric Determinantal Ideals

- Mathematics, Computer ScienceISSAC
- 2022

This paper focuses on the Sparse-FGLM algorithm, the state-of-the-art for changing ordering of Gröbner bases of zero-dimensional ideals, and studies its complexity for symmetric determinantal ideals under a variant of Fröberg's conjecture.

### Efficient linear algebra on GPUs for Gröbner bases computations

- Computer Science, Mathematics
- 2022

This work aims to compute a lexicographic Gröbner basis of the ideal spanned by f1, which generically is of the form gn = 0, xn−1 = gn−1 (xn), . . . , x1 = g1 ( xn), deggn = D.

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