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A survey on signature-based algorithms for computing Gröbner basis computations

Christian Eder 1 Jean-Charles Faugère 2
2 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria de Paris
Abstract : This paper is a survey on the area of signature-based Gröbner basis algorithms that was initiated by Faugère's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the various known variants by 3 different orderings. For this we give translations between different notations and show that besides notations many approaches are just the same. Moreover, we give a general description of how the idea of signatures is quite natural when performing the reduction process using linear algebra. This survey shall help to outline this field of active research.
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Submitted on : Monday, November 21, 2016 - 5:08:35 PM
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Christian Eder, Jean-Charles Faugère. A survey on signature-based algorithms for computing Gröbner basis computations. Journal of Symbolic Computation, Elsevier, 2016, pp.1-75. ⟨10.1016/j.jsc.2016.07.031⟩. ⟨hal-00974810v2⟩

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