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

Jean-Charles Faugère 1, 2
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
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.
keyword : groebner
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Conference papers
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https://hal.inria.fr/inria-00100995
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Submitted on : Tuesday, September 26, 2006 - 2:53:23 PM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM

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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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