Distributed Maple: parallel computer algebra in networked environments

Schreiner, Wolfgang; Mittermaier, Christian; Bósa, Károly

doi:10.1016/s0747-7171(02)00137-2

Cited by 20 publications

(23 citation statements)

References 8 publications

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“…The picture is similar for the E 8 reps 11 to 15 when investigating strong scaling from 4 to 32 nodes on HECToR; rep 11 achieves the top speedup of 548×, top efficiency of 55%, but the other reps do not scale so well. Note that for multi-phase symbolic computations with irregular and dynamic parallelism an efficiency of 40% is good, as previously reported on smaller architectures [15,16,26].…”

Section: Evaluation Of Parallel Performancesupporting

confidence: 81%

“…Several computer algebra systems offer dedicated support for parallelism (see [10,Sec 2.18] and [25]). Distributed Maple [26] provides a portable Java-based communication layer to permit interaction of Maple instances over a network. It uses future-based language constructs for synchronisation and communication, and has been used to parallelise several computational geometry algorithms.…”

Section: Related Workmentioning

confidence: 99%

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High-Performance Computer Algebra: A Hecke Algebra Case Study

Maier

Livesey

Loidl³

et al. 2014

Lecture Notes in Computer Science

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Abstract. We describe the first ever parallelisation of an algebraic computation at modern HPC scale. Our case study poses challenges typical of the domain: it is a multi-phase application with dynamic task creation and irregular parallelism over complex control and data structures. Our starting point is a sequential algorithm for finding invariant bilinear forms in the representation theory of Hecke algebras, implemented in the GAP computational group theory system. After optimising the sequential code we develop a parallel algorithm that exploits the new skeleton-based SGP2 framework to parallelise the three most computationally-intensive phases. To this end we develop a new domain-specific skeleton, parBufferTryReduce. We report good parallel performance both on a commodity cluster and on a national HPC, delivering speedups up to 548 over the optimised sequential implementation on 1024 cores.

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Section: Evaluation Of Parallel Performancesupporting

confidence: 81%

Section: Related Workmentioning

confidence: 99%

High-Performance Computer Algebra: A Hecke Algebra Case Study

Maier

Livesey

Loidl³

et al. 2014

Lecture Notes in Computer Science

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“…Chris Eilbeck began working on this problem while attending the programme in Nonlinear Waves at the Mittag-Leffler Institute in Stockholm in 2005, and he would like to thank Professor H. Holden of Trondheim and the Swedish Academy of Sciences for making this possible. Some of the calculations described in this paper were carried out using Distributed Maple [24], and we are grateful to the author of this package, Professor Wolfgang Schreiner of RISC-Linz, for help and advice.…”

Section: Acknowledgementsmentioning

confidence: 99%

Abelian functions for cyclic trigonal curves of genus 4

Baldwin

Eilbeck

Gibbons

et al. 2008

Journal of Geometry and Physics

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Abstract. We discuss the theory of generalized Weierstrass σ and ℘ functions defined on a trigonal curve of genus four, following earlier work on the genus three case. The specific example of the "purely trigonal" (or "cyclic trigonal") curve y 3 = x 5 + λ 4 x 4 + λ 3 x 3 + λ 2 x 2 + λ 1 x + λ 0 is discussed in detail, including a list of some of the associated partial differential equations satisfied by the ℘ functions, and the derivation of an addition formulae.

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“…For example, ParGap [11] is an extension of GAP which defines a similar set of parallel patterns to our basic set; the new Threads package for Maple [27] provides userlevel routines for multi-threaded programming on multicore computers; the Distributed Maple environment [38] allows the construction of Maple applications across distributed systems; Maple2g [34] uses Globus to link Maple to computational Grids; and the rather misleadingly-named gridMathematica and Mathematica Personal Grid Edition similarly support parallel cluster computing in Mathematica.…”

Section: Parallel Symbolic Computationmentioning

confidence: 99%