HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

Changing the ordering of Gröbner Bases with LLL: Case of Two Variables

Abdolali Basiri 1, 2 Jean-Charles Faugère 1, 2
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We present an algorithm for the transformation of a Gröbner basis of an ideal with respect to any given ordering into a Gröbner basis with respect to any other ordering. This algorithm is based on a modified version of the LLL algorithm. The worst case theoretical complexity of this algorithm is not better than the complexity of the FGLM algorithm; but can also give the theoretical complexity with some parameters depending on the size of the output. When the output is small then algorithm is more efficient. We also present a first implementation of the algorithm in Maple. This algorithm is restricted to the case of two variables but works also in positive dimension.
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00071841
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Tuesday, May 23, 2006 - 6:56:21 PM
Last modification on : Friday, February 4, 2022 - 3:25:28 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:40:39 PM

Identifiers

  • HAL Id : inria-00071841, version 1

Citation

Abdolali Basiri, Jean-Charles Faugère. Changing the ordering of Gröbner Bases with LLL: Case of Two Variables. [Research Report] RR-4746, INRIA. 2003. ⟨inria-00071841⟩

Share

Metrics

Record views

92

Files downloads

153