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 multiple-residue 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 extension e.g.. The parallelisation utilises algorithmic skeletons. A non-trivial example computation is also supplied.
Supported by DFG grant LO 630-3/1.
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Lobachev, O., Loogen, R. (2010). Implementing Data Parallel Rational Multiple-Residue Arithmetic in Eden. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2010. Lecture Notes in Computer Science, vol 6244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15274-0_15
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