Christian Eder
Abstract
In this paper we describe a combination of ideas to improve incremental signature-based Gröbner basis algorithms which have a big impact on their performance. Besides explaining how to combine already known optimizations to achieve more efficient algorithms, we show how to improve them even further. Although our idea has a postive effect on all kinds of incremental signature-based algorithms, the way this impact is achieved can be quite different. Based on the two best-known algorithms in this area, F5 and G2V, we explain our idea, both from a theoretical and a practical point of view.
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