Section: New Results

Highlights of the Year

Jointly with Univ. Of Kaiserslautern (C. Eder), we have released a new open source C library for linear algebra dedicated to Gröbner bases computations (see http://www-polsys.lip6.fr/~jcf/Software/index.html ). This new library opens the door to high performance applications

• The library is specialized in reducing matrices generated during Gröbner bases computations. Optimizing this reduction step is crucial for the overall computation.

• Our approach takes even more advantage of the very special structure (quasi unit-triangular sparse matrices with patterns in the data)

• We also reduce the number of operations, in a parallel friendly fashion, by changing the order of the operations in the elimination.

• We present experimental results for sequential and parallel computations on NUMA architectures. We also get good scaling up until 32 (non hyper-threaded) cores: we have speed-ups around 14 or 16.