SPIRAL : Polynomial Systems, Implementations and Algebraic Resolutions

SPIRAL (whose acrynom means Polynomial Systems, Implementations and Algebraic Resolutions) is a team of the department of Scientific Computing of the Computer Science Laboratory LIP6.

The main goal of the team is to  solve algebraic systems of equations and their applications. Our team is internationnally known as one of the leader in this field. A part of our team is involved in the INRIA/LIP6 SALSA Project whose aim is the design and the implementation of efficient algorithms solving polynomial systems. Among the fields of applications in which some results have already been obtained, we can point out simulation, control and diagnostic of parallel manipulators, error correcting codes, cryptography, image compression and biophysics.

The software and the algorithms developed in the team are among the fastest in the world. They are designed for real life applications or teaching. Some of our implementations will be integrated in the future version of Maple (MapleSoft company) thus ensuring diffusion of these tools to a wider audience. Some of our productions can be downloaded at our Software page.

Emerging new directions of research are:

• random generation of combinatorial structures and
• the interaction between symbolic and numeric computation for solving algebraic equations (joint action with the PEQUAN team of the department of Scientific Computing of LIP6).

Research thematics are more precisely described in the page Research.