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A survey on signature-based Gröbner basis computations (1404.1774v1)
Published 7 Apr 2014 in math.AC and cs.SC
Abstract: This paper is a survey on the area of signature-based Gr\"obner basis algorithms that was initiated by Faug`ere'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.