FGb

FGb/Gb libraryGb is a program (191 420 lines of C++) for computing Grobner bases, implement ”standard” algoritms. FGb (206 052 lines of C) ia an efficient program written in C for solving polynomial systems. The purpose of the FGb library is twofold. First of all, the main goal is to provide efficient implementations of state-of-the-art algorithms for computing Gröbner bases: actually, from a research point of view, it is mandatory to have such an implementation to demonstrate the practical efficiency of new algorithms. Secondly, in conjunction with other software, the FGb library has been used in various applications (Robotic, Signal Theory, Biology, Computational Geometry, . . . ) and more recently to a wide range of problems in Cryptology (for instance, FGb was explicitly used in [2, 8, 9, 4, 5] to break several cryptosystems)