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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
2 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
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.
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Submitted on : Tuesday, May 23, 2006 - 6:56:21 PM
Last modification on : Friday, September 16, 2022 - 1:45:47 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:40:39 PM


  • HAL Id : inria-00071841, version 1


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⟩



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