Polynomial System Solving and ApplicationsJean-Charles Faugere CNRS In this talk we will present new algorithms for computing polynomial systems and more specifically Groebner bases. In particular a new algorithm for computing Groebner bases without reduction to zero. We review some new applications where this techniques have been used successfully: Celestial Mechanics, Robotic, Cryptography and Error Correcting codes. It is clear from this experiments that powerful algorithms to handle various kind of symmetries are still needed. |