Abstract
We demonstrate how a new data structure for sparse distributed polynomials in the Maple 17 kernel significantly accelerates several key Maple library routines. The POLY data structure and its associated kernel operations are programmed for compactness, scalability, and low overhead. This allows polynomials to have tens of millions of terms, increases parallel speedup, and improves the performance of Maple library routines.
This work was supported by Maplesoft and the National Science and Engineering Research Council (NSERC) of Canada.
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Appendices
Appendix A
Maple code (no pivoting) for the Bareiss algorithm.
Magma code for the Bareiss algorithm.
Appendix B
Maple code for timing benchmarks.
Magma code for timing benchmarks.
Mathematica code for timing benchmarks. Note, for the fifth benchmark, we used Cancel[p/f] which was much faster than PolynomialQuotient.
Maxima code for timing benchmarks.
Sage code for timing benchmarks
Singular code for timing benchmarks.
Trip code for timing benchmarks. POLYV means recursive sparse, POLPV means recursive dense.
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Monagan, M., Pearce, R. (2014). POLY: A New Polynomial Data Structure for Maple 17. In: Feng, R., Lee, Ws., Sato, Y. (eds) Computer Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43799-5_24
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DOI: https://doi.org/10.1007/978-3-662-43799-5_24
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