A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)

Authors:
Jean Charles Faugère
Affiliations:
SPACES/LIP6/CNRS/Université Paris VI F-75252 Paris Cedex 05
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

Citing 6
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Abstract

This paper introduces a new efficient algorithm for computing Gröbner bases. We replace the Buchberger criteria by an optimal criteria. We give a proof that the resulting algorithm (called F5) generates no useless critical pairs if the input is a regular sequence. This a new result by itself but a first implementation of the algorithm F5 shows that it is also very efficient in practice: for instance previously untractable problems can be solved (cyclic 10). In practice for most examples there is no reduction to zero. We illustrate this algorithm by one detailed example.