Implementing Data Parallel Rational Multiple-Residue Arithmetic in Eden

Abstract. Residue systems present a well-known way to reduce computation cost for symbolic computation. However most residue systems are implemented for integers or polynomials. This work combines two known results in a novel manner. Firstly, it lifts an integral residue system to fractions. Secondly, it generalises a single-residue system to a multipleresidue one. Combined, a rational multi-residue system emerges. Due to the independent manner of single "parts" of the system, this work enables progress in parallel computing. We present a complete implementation of the arithmetic in the parallel Haskell extension Eden. The parallelisation utilises algorithmic skeletons. We compare our approach with Maple. A non-trivial example computation is also supplied.

• Type: Journal
• Year: 2010
• Where: CASC
• Authors: Oleg Lobachev, Rita Loogen
• Keywords: CASC 2010, Computation, Mathematics, Non-trivial Example Computation, Residue Systems