On selection of nonmultiplicative prolongations in computation of Janet bases

Authors:
V. P. Gerdt;Yu. A. Blinkov
Affiliations:
Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia 141980;Department of Mathematics and Mechanics, Saratov State University, Saratov, Russia 410071
Venue:
Programming and Computing Software
Year:
2007

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Abstract

We consider three modifications of our basic involutive algorithm for computing polynomial Janet bases. These modifications, which are related to degree-compatible monomial orders, yield specific selection strategies for nonmultiplicative prolongations. Using a standard database of benchmarks designed for testing programs computing Gröbner bases, we compare these algorithmic modifications (in terms of their efficiency) with Faugére's F 4 algorithm, which is built in the Magma computer algebra system.