On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors

Journal of the ACM (JACM)

Volumn 18, Issue 4, 1971, Pages 478-504

  Brown, W S ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

algebra; asymptotic bounds; Chinese remainder algorithm; coefficient growth; computing time analysis; Euclid's algorithm; greatest common divisors; intermediate expression swell; modular arithmetic; modular mappings; polynomial remainder sequences; polynomials; subresultants

Indexed keywords

MATHEMATICS;

EID: 0015143623     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/321662.321664     Document Type: Article

References (13)

1. Knuth, D. E. The Art of Computer Programming. Vol. 2: Seminumerical Algorithms. Addison-Wesley, Reading, Mass., 1969.
2. Sammet J. E., et al. Symbol manipulation. Comm. ACM 9 (Aug. 68), 547-643.
3. Householder, A. S. Bigradients and the problem of Routh and Hurwitz, SIAM Rev. 10 (Jan. 1968), 56-66.
4. Householder, A. S., and Stewart, G. W., III. Bigradients, Hankel determinants, and the Padé table. In Constructive Aspects of the Fundamental Theorem of Algebra, B. Dejon and P. Henrici, Eds. Wiley-Interscience, New York, 1969, pp. 131-150.
5. Uspensky, J. V. Theory of Equations, McGraw-Hill, New York, 1948.
6. Birkhoff G., and MacLane, S. A Survey of Modern Algebra, 3rd ed. Macmillan, New York, 1965.
7. Collins, G. E. Subresultants and reduced polynomial remainder sequences. J. ACM 14 (Jan. 1967), 128-142.
8. Brown W. S., and Traub, J. F. On Euclid's algorithm and the theory of subresultants.J. ACM 18 (Oct. 1971), 505-514.
9. Goldstein A. J., and Graham, R. L. A Hadamard type bound on the coefficients of a determinant of analytic functions (to be published).
10. Collins, G. E. The calculation of multivariate polynomial resultants. In Proc. 2nd Symposium on Symbolic and Algebraic Manipulation. ACM, New York, 1971, pp. 212-222.
11. J. ACM 18 (Oct. 1971), 515-532.
12. Erdélyi, A. Asymptotic Expansions. Dover, New York, 1956.
13. Proc. 2nd Symposium on Symbolic and Algebraic Manipulation. ACM, New York, 1971, Chs. 3 and 7.