Parallel computation of Grobner bases in the Weyl algebra
Interactive Parallel Computation in Support of Research in Algebra, Geometry and Number Theory
January 29,2007 01:30 PM to 02:00 PM
Speakers:
Leykin, Anton
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Abstract: |
The usual machinery of Grobner bases can be applied to non-commutative algebras of the so-called solvable type. One of them, the Weyl algebra, plays the central role in the computations with $D$-modules. The practical complexity of the Grobner bases computation in the Weyl algebra is much higher than in the (commutative) polynomial rings, therefore, calling naturally for parallel computation. We have developed an algorithm to perform such computation employing the master-slave paradigm. Our implementation, which has been carried out in C++ using MPI, draws ideas from both Buchberger algorithm and Faugere's $F_4$. It exhibits better speedups for the Weyl algebra in comparison to polynomial problems of the similar size. |
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