Concrete mathematics: a foundation for computer science
Concrete mathematics: a foundation for computer science
Algorithms for computer algebra
Algorithms for computer algebra
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Polynomial Algorithms in Computer Algebra
Polynomial Algorithms in Computer Algebra
Distributed Symbolic Computation with DTS
IRREGULAR '95 Proceedings of the Second International Workshop on Parallel Algorithms for Irregularly Structured Problems
Parallel Computation of Modular Multivariate Polynominal Resultants on a Shared Memory Machine
CONPAR 94 - VAPP VI Proceedings of the Third Joint International Conference on Vector and Parallel Processing: Parallel Processing
The calculation of multivariate polynomial resultants
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
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Polynomial resultants are of fundamental importance in symbolic computations, especially in the field of quantifier elimination. In this paper we show how to compute the resultant $\ensuremath\operatorname{res}_y(f,g)$ of two bivariate polynomials $f,g\in\ensuremath\mathbb{Z}[x,y]$ on a CUDA-capable graphics processing unit (GPU). We achieve parallelization by mapping the bivariate integer resultant onto a sufficiently large number of univariate resultants over finite fields, which are then lifted back to the original domain. We point out, that the commonly proposed special treatment for so called unlucky homomorphisms is unnecessary and how this simplifies the parallel resultant algorithm. All steps of the algorithm are executed entirely on the GPU. Data transfer is only used for the input polynomials and the resultant. Experimental results show the considerable speedup of our implementation compared to host-based algorithms.