Abstract
This paper reports our experience in parallelizing a modular algorithm for computing multivariate polynomial resultants over ℤp. The modular algorithm has the well-known scheme of “divide-conquercombine” where the “conquer” phase is straightforwardly parallelizable. But the “combine” phase is structurally sequential, and requires certain modifications for efficient parallelization. We describe and compare various different parallelization schemes (in particular for the combine phase). The variants of the algorithm have been implemented on top of the Paclib kernel which provides C-primitives for task creation and non-deterministic wait on a shared memory machine.
Supported by Austrian Science Foundation on Parallel Symbolic Computation (S5302-PHY)
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
B. Buchberger, G. Collins, M. Encarnación, H. Hong, J. Johnson, W. Krandick, R. Loos, A. Mandache, A. Neubacher, and H. Vielhaber. A SACLIB Primer. Technical Report 92-34, RISC-Linz, Johannes Kepler University, Linz, Austria, 1992.
B. W. Char. Progress Report on a System for General-Purpose Parallel Symbolic Algebraic Computation. In Int. Symposium on Symbolic and Algebraic Computation (ISSAC90), pages 96–103, Tokyo, August 20–24, 1990. ACM Press.
G. E. Collins. The Calculation of Multivariate Polynomial Resultants. Journal of the ACM, 18:515–532, 1971.
H. Hong. Efficient Method for Analyzing Topology of Plane Real Algebraic Curves. In Proceedings of IMACS-SC 93, Lille, June 1993.
H. Hong, A. Neubacher, and W. Schreiner. The Design of the SACLIB/PACLIB Kernels. In A. Miola, editor, Int. Symposium on Design and Implementation of Symbolic Computation System (DISCO 93), volume 722 of Lecture Notes in Computer Science, pages 288–302, Gmunden, September 15–17, 1993. Springer.
H. Hong, W. Schreiner, A. Neubacher, K. Siegl, H.-W. Loidl, T. Jebelean, and P. Zettler. PACLIB User Manual. Technical Report 92-32, RISC-Linz, Johannes Kepler University, Linz, Austria, May 1992.
W. Küchlin. PARSAC-2: A Parallel SAC-2 Based on Threads. In S. Sakata, editor, Eighth Int. Symposium on Applied Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC8), volume 508 of Lecture Notes in Computer Science, pages 206–217, Tokyo, August 1990. Springer.
W. Küchlin. On the Multi-Threaded Computation of Integral Polynomial Greatest Common Divisors. In S. M. Watt, editor, Int. Symposium on Symbolic and Algebraic Computation (ISSAC91), Bonn, July 15–17, 1991. ACM Press.
W. Küchlin and J. Ward. Experiments with Virtual C Threads. In 4th IEEE Symposium on Parallel and Distributed Processing, Arlington, December, 1992. IEEE Press.
R. G. K. Loos. Computing in Algebraic Extensions. In B. Buchberger, G. E. Collins, and R. G. K. Loos, editors, Computer Algebra, Symbolic and Algebraic Computation, pages 173–187. Springer, 1982.
E. Mohr, D. A. Kranz, and R. H. Halstead Jr. Lazy Task Creation: A Technique for Increasing the Granularity of Parallel Programs. In 1990 ACM Symposium on Lisp and Functional Programming, pages 185–197, Nice, June 27–29, 1990.
J. L. Roch. An Environment for Parallel Algebraic Computation. In R. E. Zippel, editor, Computer Algebra and Parallelism — Second Int. Workshop on Parallel Algebraic Computation, volume 584 of Lecture Notes in Computer Science, pages 33–50, Ithaca, May 1990. Springer.
W. Schreiner. Virtual Tasks for the PACLIB Kernel. In Joint Int. Conference on Vector and Parallel Processing (CONPAR94 — VAPP VI), Lecture Notes in Computer Science, Linz, September 6–8, 1994. Springer. Also: Technical Report 94-02, RISC-Linz.
S. Seitz. Parallel Algorithm Development. In J. Della Dora and J. Fitch, editors, Computer Algebra and Parallelism, pages 223–232. Academic Press, June 1988.
K. Siegl. ∥MAPLE∥ — A System for Parallel Symbolic Computation. In H. M. Alnuweiri, editor, Parallel Systems Fair at the Seventh Int. Parallel Processing Symposium, pages 62–67, Newport Beach, April 14, 1993.
P. Wang. Parallel Univariate Polynomial Factorization on Shared-Memory Multiprocessors. In S. Watanabe and M. Nagata, editors, Int. Symposium on Symbolic and Algebraic Computation (ISSAC90), pages 145–151. Addison-Wesley, August 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hong, H., Loidl, H.W. (1994). Parallel computation of modular multivariate polynomial resultants on a shared memory machine. In: Buchberger, B., Volkert, J. (eds) Parallel Processing: CONPAR 94 — VAPP VI. VAPP CONPAR 1994 1994. Lecture Notes in Computer Science, vol 854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58430-7_29
Download citation
DOI: https://doi.org/10.1007/3-540-58430-7_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58430-8
Online ISBN: 978-3-540-48789-0
eBook Packages: Springer Book Archive