Singular/GPI-Space Framework

 

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Massively parallel computations in computer algebra
  • GPI-Space is a workflow management system, created and successfully applied to problems in high performance numerical simulation by the Competence Center High Performance Computing of Fraunhofer ITWM. We combine Singular with GPI-Space to create a way of performing massively parallel computations in computer algebra. 
  • Our approach is based on the idea of separating computation and coordination. While Singular is used as the computational backend, the coordination is done by GPI-Space.
  • GPI-Space uses the language of Petri nets to model algorithms in the coordination layer.
  • The Singular/GPI-Space framework can be used on anything ranging from a personal computer and compute servers to ultrascale machines. In applications, it scales efficiently up to thousands of cores on HPC clusters.
  • Applications arise, so far, from algebraic geometry (certifying smoothness, resolution of singularities), tropical geometry (computing of tropicalizations with finite symmetries), geometric invariant theory (computing GIT-fans with finite symmetries), high energy physics (computing integration-by-parts identities for Feynman integrals), and condensed matter physics.
  • While relying on GPI-Space allows us to apply state-of-the-art parallelization infrastructure when using Singular, our close collaboration has, in turn, also lead to introducing new programming constructs in GPI-Space, and to developing an open source version of GPI-Space.
  • An Open Source Version of GPI-Space has been released by ITWM in Sept. 2020 (this software is actively being tested on CentOS Linux (Versions 6, 7, 8) and Ubuntu (Versions 18.04 LTS, 20.04 LTS), but various other distributions will work as well). A first end user version of the Singular/GPI-Space Framework has been released in Dec. 2020, see Download. In the future we will gradually add more of our code to this version, and of course develop new features.
  • The Singular/GPI-Space framework code base is currently migrating to the supercomputing package manager Spack, which provides an easy one-line installer experience in any environment from a personal computer to a supercomputer setting. Our repository with Spack packages currently provides some of our applications, e.g., pfd-parallel, and all dependencies including Singular, GPI-Space, GPI-2 and Flint.
  • Future plans include connecting GPI-Space to the evolving system OSCAR, which builds on and extends the four cornerstone systems GAP, Singular, polymake, and Antic.

    Supported by DFG     SFB-TRR 195 and Forschungsinitiative Rheinland-Pfalz. 

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