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

Authors:
Abdolali Basiri;Jean-Charles Faugère
Affiliations:
Spaces/Lip6/Loria/CNRS/Université ParisVI, Paris;Spaces/Lip6/Loria/CNRS/Université ParisVI, Paris Cedex
Venue:
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Year:
2003

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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.