Distributed Parallel Groebner Bases Computation

Abstract

This paper considers the implementation of parallel Gröbner bases algorithms on distributed memory parallel computers like todays high performance computing clusters (HPC) in the Java computer algebra library (JAS). The implementation of Gröbner bases algorithms is part of the essential building blocks for any computation in algebraic geometry. There are various implementations of these algorithms in procedural programming languages. Our aim is an implementation in a modern object oriented programming language with generic data types, as it is provided by Java programming language. The proposed middle-ware uses a distributed list for the communication of the reduction bases and a distributed thread pool for running the reduction engines in different computers. Java object serialization is used to encode polynomial objects for network transport via Java networking facilities.