Parallel polynomial operations on SMPs: An overview

Journal of Symbolic Computation

Volumn 21, Issue 4-6, 1996, Pages 397-410

  Wang, Paul S ^a  

^a KENT STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030118195     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1996.0021     Document Type: Review

References (26)

1. Beauzamy, B., Trevisan, V., Wang, P. (1993). Polynomial factorization: sharp bounds, efficient algorithms. J. Symbolic Computation, 15:393-413.
2. Buchberger, B. Collins, G.E. et al. (1993). SACLIB 1.1 User's Guide. RISC-Linz Technical Report No 93-19, Research Institute for Symbolic Computation, Kepler University, A-4040 Linz, Austria.
3. Char, B. Geddes, K., Gonnet, G. (1989). GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation. J. Symbolic Computation, 7:31-48,
4. Dora, D., Fitch, J. (eds) (1988). Computer Algebra and Parallelism, San Diego, CA: Academic Press,
5. Geist, A., et al. (1993). PVM 3 User's Guide And Reference Manual. ORNL/TM-12187, Oak Ridge National Laboratory.
6. Granlund, T. (1991). GNU MP: The GNU Multiple Precision Arithmetic Library, Free Software Foundation.
7. Gray, S., Kajler, N., Wang, P. (1996). Design and implementation of MP, a protocol for efficient exchange of mathematical expressions, J. Symbolic Computation, to appear.
8. Knuth, D. (1980). The Art of Computer Programming. Vol. 2:Semi-numerical Algorithms, Reading, MA: Addison-Wesley,
9. Moenck, R. (1976). Practical Fast Polynomial Multiplication. Proc. SYMSAC'76, 136-145.
10. Moore, P., Norman, A. (1981). Implementing a Polynomial Factorization and GCD Package. Proc. 1981 ACM Symposium on Symbolic and Algebraic Computation, 109-116.
11. Moses, J., Yun, D. (1973). The EZGCD Algorithm. Proc., ACM National Conference, 159-166.
12. Musser D. (1976). Multivariate polynomial factorization. JACM 22:291-308.
13. Rayes, M., Weber, K., Wang, P. (1994). Parallelization of The Sparse Modular GCD Algorithm for Multivariate Polynomials on Shared Memory Multiprocessors, Proc. ISSAC'94, Oxford, UK, 66-73,
14. Rayes, M., Wang P. (1994). Parallel GCD for Sparse Multivariate Polynomials on Shared Memory Multiprocessors, Proc. PASCO'94 RISC/Linz, 326-335,
15. Serpette, B., Vuillemin, J, Hervé, J. (1985). BigNum: A Portable and Efficient Package for Arbitrary-Precision Arithmetic. Digital Equipment Corp., Paris Research Laboratory, Av. Victor Hugo. 92563
16. Wang, P., Trager, B. (1979). New Algorithms for polynomial square-free decomposition over the integers. SIAM J. Computing, 8.3:300-305.
17. Wang, P. (1978). An improved multivariate polynomial factoring algorithm. Mathematics of computation, 144:1215-1231.
18. Wang, P. (1979). Analysis of the p-adic Construction of Multivariate Correction Coefficients in Polynomial Factorization: Iteration vs. Recursion. LNCS, 72:291-300. Springer-Verlag.
19. Wang, P. (1990). Parallel univariate polynomial factorization on shared-memory multiprocessors. Proc. of the ISSAC'90, Addison-Wesley, 145-151.
20. Wang, P. (1991). Symbolic Computation and Parallel Software. Proc. First International Conference of the Austrian Center for Parallel Computation. LNCS, Parallel Computation, 591:316-337 Springer-Verlag.
21. Wang, P. (1992). Parallel Univariate p-adic Lifting on Shared-Memory Multiprocessors. Proc. ISSAC'92, 168-176.
22. Wang, P. (1994). Parallel Polynomial Operations: a progress report. Proc. PASCO'94, RISC/Linz, 394-404.
23. Wang, P. (1996). Tools to Aid PVM Users, PVM Users Meeting, Feb. 26-27, Albuquerque, New Mexico (http://monkey.mcs.kent.edu/~pwang/).
24. Zassenhaus, H. (1969). On Hensel factorization. J. Number Theory 1:291-311.
25. Zippel, R. (ed) (1990). Computer Algebra and Parallelism, Proc. Second International Workshop, Ithaca, USA, Springer-Verlag.
26. Zippel, R. (1979). Probabilistic Algorithms for Sparse Polynomials. PhD. Thesis, Massachusetts Institute of Technology.