Integer matrix diagonalization

Journal of Symbolic Computation

Volumn 24, Issue 3-4, 1997, Pages 399-408

  Havas, George ^a   Majewski, Bohdan S ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031232429     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1996.0141     Document Type: Article

References (18)

1. Blankinship, W.A. (1963). A new version of the Euclidean algorithm. Amer. Math. Monthly 70, 742-745.
2. Bradley, G.H. (1970). Algorithm and bound for the greatest common divisor of n integers. Commun. ACM 13, 433-436.
3. Frumkin, M.A. (1976). An application of modular arithmetic to the construction of algorithms for solving systems of linear equations. Soviet Math. Dokl. 17, 1165-1168.
4. Giesbrecht, M. (1995). Fast computation of the Smith normal form of an integer matrix. In A.H.M. Levelt, (ed.), ISSAC'95 (Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation). New York: ACM Press, pp. 110-118.
5. Havas, G., Holt, D.F., Rees, S. (1993). Recognizing badly presented Z-modules. Linear Algebra Appl. 192, 137-163.
6. Havas, G., Majewski, B.S. (1994). Hermite normal form computation for integer matrices. Congressus Numerantium 105, 87-96.
7. Havas, G., Majewski, B.S. (1995). A hard problem that is almost always easy. Algorithms and Computation, LNCS 1004, 216-223.
8. Havas, G., Majewski, B.S., Matthews, K.R. (1994). Extended gcd algorithms. Technical Report 302, Department of Computer Science, The University of Queensland.
9. Kannan, R., Bachem, R. (1979). Polynomial time algorithms for computing Smith and Hermite normal forms of an integer matrix. SIAM J. Comput. 8, 499-507.
10. Knuth, D.E. (1973). The Art of Computer Programming, Vol. 2: Seminumerical Algorithms. Reading: Addison-Wesley, 2nd edition.
11. Kronecker, L. (1901). Vorlesung über Zahlentheorie I. Liepzig: Teubner.
12. Majewski, B.S., Havas, G. (1994). The complexity of greatest common divisor computations. Algorithmic Number Theory, LNCS 877, 184-193.
13. Majewski, B.S., Havas, G. (1995). A solution to the extended gcd problem. In A.H.M. Levelt, (ed.), ISSAC'95 (Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation). New York: ACM Press, pp. 248-253.
14. Niven, I., Zuckerman, H.S., Montgomery, H.L. (1991). An Introduction to the Theory of Numbers. John Wiley & Sons, Inc., 5th edition.
15. Rosen, K.H. (1992). Elementary Number Theory and its Applications. Reading: Addison-Wesley, 3rd edition.
16. Rose, D.J., Tarjan, R.E. (1978). Algorithmic aspects of vertex elimination on directed graphs. SIAM J. Appl. Math. 34, 176-197.
17. Smith, H.J.S (1861). On systems of linear indeterminate equations and congruences. Philos. Trans. Royal Soc. London cli, 293-326. Reprinted in The Collected Mathematical Papers of Henry John Stephen Smith, Volume 1. New York: Chelsea (1965).
18. van Emde Boas, P. (1981). Another NP-complete partition problem and the complexity of computing short vectors in a lattice. Technical Report MI/UVA 81-04, The University of Amsterdam.