Parallel and distributed Gröbner bases computation in JAS

This paper considers parallel Gröbner bases al-gorithms on distributed memory parallel comput-ers with multi-core compute nodes. We summa-rize three different Gröbner bases implementations:shared memory parallel, pure distributed memoryparallel and distributed memory combined withshared memory parallelism. The last algorithm,called distributed hybrid, uses only one controlcommunication channel between the master nodeand the worker nodes and keeps polynomials inshared memory on a node. The polynomials aretransported asynchronous to the control-flow of thealgorithm in a separate distributed data structure.The implementation is generic and works for allimplemented (exact) fields. We present new perfor-mance measurements and discuss the performanceof the algorithms.