High-Performance Computer Algebra: A Hecke Algebra Case Study

  • Patrick Maier
  • Daria Livesey
  • Hans-Wolfgang Loidl
  • Phil Trinder
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8632)


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.


Parallel Algorithm Computer Algebra Symbolic Computation Laurent Polynomial Reduce Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Patrick Maier
    • 1
  • Daria Livesey
    • 2
  • Hans-Wolfgang Loidl
    • 3
  • Phil Trinder
    • 1
  1. 1.School of Computing ScienceUniversity of GlasgowGlasgowUK
  2. 2.School of Natural and Computing SciencesUniversity of AberdeenAberdeenUK
  3. 3.School of Mathematical and Computer SciencesHeriot-Watt UniversityEdinburghUK

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