A modification of Shanks’ baby-step giant-step algorithm
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- by David C. Terr PDF
- Math. Comp. 69 (2000), 767-773 Request permission
Abstract:
I describe a modification to Shanks’ baby-step giant-step algorithm for computing the order $n$ of an element $g$ of a group $G$, assuming $n$ is finite. My method has the advantage of being able to compute $n$ quickly, which Shanks’ method fails to do when the order of $G$ is infinite, unknown, or much larger than $n$. I describe the algorithm in detail. I also present the results of implementations of my algorithm, as well as those of a similar algorithm developed by Buchmann, Jacobson, and Teske, for calculating the order of various ideal classes of imaginary quadratic orders.References
- Johannes Buchmann, Michael J. Jacobson Jr., and Edlyn Teske, On some computational problems in finite abelian groups, Math. Comp. 66 (1997), no. 220, 1663–1687. MR 1432126, DOI 10.1090/S0025-5718-97-00880-6
- Donald E. Knuth, The art of computer programming. Volume 3, Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1973. Sorting and searching. MR 0445948
- “Dave’s Cool Java Home Page", http://www.geocities.com/CapeCanaveral /LaunchPad/5318 (1998).
Additional Information
- David C. Terr
- Affiliation: 2614 Warring St. #7, Berkeley, CA 94704
- Email: davidcterr@aol.com
- Received by editor(s): September 4, 1996
- Received by editor(s) in revised form: May 30, 1998
- Published electronically: March 4, 1999
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 69 (2000), 767-773
- MSC (1991): Primary 68P10, 20C40
- DOI: https://doi.org/10.1090/S0025-5718-99-01141-2
- MathSciNet review: 1653994