Improving the multiprecision Euclidean algorithm

1. B. Buchberger. Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory. In Bose and Reidel, editors, Recent trends in Multidimensional Systems, pages 184–232, Dordrecht-Boston-Lancaster, 1985. D. Reidel Publishing Company.

   Google Scholar 

2. B. Buchberger and T. Jebelean. Parallel rational arithmetic for Computer Algebra Systems: Motivating experiments. In 3rd Scientific Workshop of the Austrian Center for Parallel Computation, Weinberg, Austria, March 1992. Report ACPC/TR 93-3, February 1993.

   Google Scholar 

3. G. E. Collins. Lecture notes on arithmetic algorithms, 1980. Univ. of Wisconsin.

   Google Scholar 

4. M. Encarnacion. A Lehmer-type improvement of the modular residue to rational conversion. Technical report, RISC-Linz, 1993. To appear.

   Google Scholar 

5. T. Granlund. GNU MP: The GNU multiple precision arithmetic library, 1991.

   Google Scholar 

6. T. Jebelean. A Generalization of the Binary GCD Algorithm. In ISSAC'93: International Symposium on Symbolic and Algebraic Computation, Kiev, Ukraine, July 1993.

   Google Scholar 

7. T. Jebelean. Comparing Several GCD Algorithms. In ARITH-11: IEEE Symposium on Computer Arithmetic, Windsor, Canada, June 1993.

   Google Scholar 

8. D. E. Knuth. The art of computer programming, volume 2. Addison-Wesley, 2 edition, 1981.

   Google Scholar 

9. D. H. Lehmer. Euclid's algorithm for large numbers. Am. Math. Mon., 45:227–233, 1938.

   Google Scholar 

10. R. T. Moenck. Fast computation of GCDs. In ACM Vth Symp. Theory of Computing, pages 142–151. ACM, 1973.

    Google Scholar 

11. W. Neun and H. Melenk. Very large Gröbner basis calculations. In Zippel, editor, Computer algebra and parallelism. Proceedings of the second International Workshop on Parallel Algebraic Computation, pages 89–100, Ithaca, May 1990. LNCS 584, Springer Verlag.

    Google Scholar 

12. A. Schönhage. Schnelle Berechung von Kettenbruchentwicklugen. Acta Informatica, 1:139–144, 1971.

    Article  Google Scholar 

13. J. Sorenson. Two fast GCD algorithms. Submitted to J. of Algorithms, 1993.

    Google Scholar 

14. J. Stein. Computational problems associated with Racah algebra. J. Comp. Phys., 1:397–405, 1967.

    Article  Google Scholar 

15. P. S. Wang, M. J. T. Guy, and J. H. Davenport. P-adic reconstruction of rational numbers. ACM SIGSAM Bulletin, 16(2):2–3, May 1982.

    Google Scholar 

16. Ken Weber. The accelerated integer gcd algorithm. Technical report, Kent State University, 1993. To appear.

    Google Scholar 

Download references