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A chapter from "The Algorithm Design Manual" by Steven S. Skiena.
http://www.cs.sunysb.edu/~algorith/major_section/1.2.shtml
Notes and Javascript illustrations by Robert Campbell.
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Basics of Computational Number Theory This document is a gentle introduction to computational number theory. The plan of the paper is to first give a quick overview of arithmetic in the modular integers. Throughout, we will emphasize computation and practical results rather than delving into...Lecture notes by Robert Campbell, December 1997.
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Computational Number Theory This is a short collection of documents which provides an introduction to computational number theory. The first text provides a simple gloss of the subject, emphasizing results at the expense of theory, what instead of why. The second text will...Provided by the organizers of the MSRI Fall 2000 research program.
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Suggested readings in Algorithmic number theory Algorithmic number theory This list was provided by the organizers of the Fall 2000 program in Algorithmic number theory. Editor: Adleman, Leonard M Huang, Ming-Deh A. Title: Algorithmic number theory first international symposium, ANTS-I, Ithaca, NY, USA, May 6-9, 1994...Papers on the LLL algorithm and its applications collected by François Koeune.
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The LLL Algorithm This page is only under development. Any suggestion to improve it is of course welcome just drop me an e-mail Some Interesting references about LLL Understanding LLL Maybe the best reference to understand how LLL works is the original paper...Interesting problems, usually requiring extensive verifications or enumerations, to occupy the idle CPU time of workstations and personal computers. Compiled by Tomás Oliveira e Silva.
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Computational projects Latin locution was found in the home page of David Bailey Introduction Long ago, I decided to find interesting problems, usually requiring extensive verifications and/or enumerations, to occupy the idle CPU time of most workstations and personal computers in my...Notes by Al Sethuraman.
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These notes were written as part of a seminar that I ran during Fall 2000 at CSUN. Algorithmic Number Theory I Cyclicity of units of Z/p^n for odd p, Carmichael numbers. Algorithmic Number Theory II Primality testing, Solovay-Strassen test, Quadratic...Connected with divisibility and factoring.
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Some number records For records concerning the number of known digits of constants like Pi, E, please see the nice Table of Mathematical Constants compiled by Steve Finch. Take also a look at the Number Theory Seminar at IECN (Nancy Aliquot sequences Famous...Some of the conjectures and open problems motivated by the "PRIMES is in P" papers, compiled at the AIM.
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Future directions in algorithmic number theory This web page highlights some of the conjectures and open problems concerning Future directions in algorithmic number theory. If you would like to print a hard copy of the whole outline, you can download...Maintained by Keith Matthews. Papers, examples, pseudocode.
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KEITH MATTHEWS LLL PAGE Hermite normal form algorithms via lattice basis reduction, G. Havas, B.S. Majewski, K.R. Matthews, Experimental Mathematics, Vol 7 (1998) 125-136. I believe these algorithms are among the best for obtaining (a) small multipliers for the extended gcd problems and more...Enter two positive integers, and click the button to see the operations of the Euclidean Algorithm.
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Visible Euclidean Algorithm This computes the greatest common divisor of two given integers via the Euclidean Algorithm, showing all the steps. The greatest common divisor is explicitly noted at the bottom. Be sure to keep the integers 18 digits or smaller, and you...