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Conference Papers Year : 2002

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

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 F_5 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.

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Other [cs.OH]
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Dates and versions

inria-00100995 , version 1 (26-09-2006)

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Jean-Charles Faugère. A new efficient algorithm for computing Gröbner bases without reduction to zero F5. International Symposium on Symbolic and Algebraic Computation Symposium - ISSAC 2002, Jul 2002, Villeneuve d'Ascq, France. pp.75-83, ⟨10.1145/780506.780516⟩. ⟨inria-00100995⟩
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