On selection of nonmultiplicative prolongations in computation of Janet bases
Vladimir P. Gerdt, Yu. A. Blinkov · Programming and Computer Software · 2007
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.