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Published in:
2021 | OriginalPaper | Chapter
Parallel Computation of Gröbner Bases on a Graphics Processing Unit
Authors : Mark Hojnacki, Andrew Leeseberg, Jack O’Shaughnessy, Michael Dauchy, Alan Hylton, Leah Gold, Janche Sang
Published in: Advances in Parallel & Distributed Processing, and Applications
Publisher: Springer International Publishing
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Abstract
Solving polynomial systems of equations of both many degrees and variables is not a simple computation. A method of solving these systems is to transform them into a Gröbner basis. Gröbner bases have desirable mathematical properties that make it possible to solve systems of polynomial equations. The computations necessary to compute Gröbner bases are many and can sometimes take days if not longer. Existing implementations are unable to handle the high degree polynomial systems necessary for specialized applications. Graphics Processing Units specialize in fast parallel computations by means of using many (several hundred to a couple thousand) computing cores. Utilizing these cores in parallel allows difficult problems to be solved quickly, versus using a Central Processing Unit, when optimized properly. The goal of this project is to implement a Gröbner basis algorithm that is optimized for GPUs which in turn will allow for faster computations of Gröbner bases.