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

Ali Basiri 1 Jean-Charles Faugère 1
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.
Type de document :
Communication dans un congrès
Hoon Hong. International Symposium on Symbolic and Algebraic Computation - ISSAC 03, 2003, Philadelphie, USA, ACM Press, pp.23-29, 2003
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https://hal.inria.fr/inria-00099732
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Soumis le : mardi 26 septembre 2006 - 09:40:45
Dernière modification le : jeudi 11 janvier 2018 - 06:20:00

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  • HAL Id : inria-00099732, version 1

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Ali Basiri, Jean-Charles Faugère. Changing the ordering of Grobner Bases with LLL: Case of Two Variables. Hoon Hong. International Symposium on Symbolic and Algebraic Computation - ISSAC 03, 2003, Philadelphie, USA, ACM Press, pp.23-29, 2003. 〈inria-00099732〉

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