Section: New Software and Platforms

TinyGB

• Author: Pierre-Jean Spaenlehauer

• Contact: Pierre-Jean Spaenlehauer

• URL: https://gforge.inria.fr/projects/tinygb/

• Licence: LGPL-3.0+

TinyGB is a software implementing tools for computing Gröbner bases of ideals in polynomial rings over finite fields. It has been released in April 2016.

It is not competitive with state-of-art software for computations over small prime fields. However, for polynomial systems over $\mathbb{Z}/p\mathbb{Z}$, with $p>2^{31}$, its timings are competitive with the computer algebra system Magma-2.22-2 (although the Magma is much better in terms of memory requirements). This is due to the fact that TinyGB relies on the library MPFQ (developed in the Caramba team) for the efficient arithmetic over large prime fields. For instance, computing the grevlex Gröbner basis of a system of 13 dense homogeneous quadratic equations in 13 variables over the field $\mathbb{Z}/(2^{31}+11)\mathbb{Z}$ can be achieved within 907 seconds with TinyGB , whereas Magma-2.22-2 requires 4459 seconds (on an Intel Core i5-4590@3.30GHz).

The distribution of TinyGB contains the libraries OpenBLAS , FFLAS-FFPACK and MPFQ .