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Changing the ordering of Gröbner bases with LLL: case of two variables

Abdolali Basiri 1 Jean-Charles Faugère 1 
1 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 : Friday, June 2, 2017 - 11:32:22 AM
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Abdolali Basiri, Jean-Charles Faugère. Changing the ordering of Gröbner bases with LLL: case of two variables. ISSAC 2003 - International Symposium on Symbolic and Algebraic Computation, Aug 2003, Philadelphia, PA, United States. pp.23-29, ⟨10.1145/860854.860866⟩. ⟨hal-01531992⟩



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