Roland Engdahl: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=5758
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 25 Jul 2017 22:37:37 GMTTue, 25 Jul 2017 22:37:37 GMTNew applications published by Roland Engdahlhttp://www.mapleprimes.com/images/mapleapps.gifRoland Engdahl: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=5758
Chinese Remainder Theorem
https://www.maplesoft.com/applications/view.aspx?SID=99372&ref=Feed
<p>Let m[1],m[2],...,m[n] be pairwise relatively prime integers</p>
<p> Then the simultaneous congruence</p>
<p>x = r[1] mod m[1]</p>
<p>...</p>
<p>x = r[n] mod m[n]</p>
<p>has a unique solution modulo the product m[1].m[2]- -.-. .m[n]</p><img src="/view.aspx?si=99372/maple_icon.jpg" alt="Chinese Remainder Theorem" align="left"/><p>Let m[1],m[2],...,m[n] be pairwise relatively prime integers</p>
<p> Then the simultaneous congruence</p>
<p>x = r[1] mod m[1]</p>
<p>...</p>
<p>x = r[n] mod m[n]</p>
<p>has a unique solution modulo the product m[1].m[2]- -.-. .m[n]</p>99372Wed, 24 Nov 2010 05:00:00 ZRoland EngdahlRoland EngdahlMEANS
https://www.maplesoft.com/applications/view.aspx?SID=34930&ref=Feed
<p>Elementary calculations of means with classroom examples, showing proofs of inequalities between means, theoretical and by geometry.</p>
<p>One solutiion for an extremely difficult puzzle illustrating inequality in three dimensions.</p>
<p>Iteration on mixed arithmetic-geometric-harmonic means</p>
<p>Calculation values of elliptic integrals by mixed iteration.</p><img src="/view.aspx?si=34930/means.png" alt="MEANS" align="left"/><p>Elementary calculations of means with classroom examples, showing proofs of inequalities between means, theoretical and by geometry.</p>
<p>One solutiion for an extremely difficult puzzle illustrating inequality in three dimensions.</p>
<p>Iteration on mixed arithmetic-geometric-harmonic means</p>
<p>Calculation values of elliptic integrals by mixed iteration.</p>34930Wed, 09 Dec 2009 05:00:00 ZRoland EngdahlRoland EngdahlStopping Patterns in random Sequences
https://www.maplesoft.com/applications/view.aspx?SID=5643&ref=Feed
Theory for one and two stopping patterns.
Programs for theoretical values and simulation.
Winning ways for a game with two stopping patterns, including graphs and strategy.
Asymptotic values of probabilities for one stopping pattern.
Relations between median and mean waiting times.<img src="/view.aspx?si=5643/stoppingpatternsforrandomsequences_344.jpg" alt="Stopping Patterns in random Sequences" align="left"/>Theory for one and two stopping patterns.
Programs for theoretical values and simulation.
Winning ways for a game with two stopping patterns, including graphs and strategy.
Asymptotic values of probabilities for one stopping pattern.
Relations between median and mean waiting times.5643Wed, 06 Feb 2008 00:00:00 ZRoland EngdahlRoland EngdahlFirst Digit Simulation
https://www.maplesoft.com/applications/view.aspx?SID=5562&ref=Feed
The simulations examine the distribution of the first (nonzero) digits in the products of 2, 3 ...
factors created from random numbers.<img src="/view.aspx?si=5562//applications/images/app_image_blank_lg.jpg" alt="First Digit Simulation" align="left"/>The simulations examine the distribution of the first (nonzero) digits in the products of 2, 3 ...
factors created from random numbers.5562Wed, 19 Dec 2007 00:00:00 ZRoland EngdahlRoland EngdahlPsedudoprimes
https://www.maplesoft.com/applications/view.aspx?SID=4816&ref=Feed
In order to prove primality of a number, previously we required a list of primes. Eratosthenes, about 230 B.C., created his famous sieve, The Sieve of Eratosthenes. Nowadays we have methods to perform sieve and store a table of primes on a computer system.
Fermat, 1640 , described one characteristic of primes in his famous theorem. The converse of this theorem is however not true. There are composite numbers which comply with this characteristic These numbers are called pseudoprimes.
This application provides examples and programs about primes, pseudoprimes, Carmichael numbers, strong pseudoprimes and primality testing. Only definitions of the concepts are included.<img src="/view.aspx?si=4816//applications/images/app_image_blank_lg.jpg" alt="Psedudoprimes" align="left"/>In order to prove primality of a number, previously we required a list of primes. Eratosthenes, about 230 B.C., created his famous sieve, The Sieve of Eratosthenes. Nowadays we have methods to perform sieve and store a table of primes on a computer system.
Fermat, 1640 , described one characteristic of primes in his famous theorem. The converse of this theorem is however not true. There are composite numbers which comply with this characteristic These numbers are called pseudoprimes.
This application provides examples and programs about primes, pseudoprimes, Carmichael numbers, strong pseudoprimes and primality testing. Only definitions of the concepts are included.4816Tue, 05 Sep 2006 00:00:00 ZRoland EngdahlRoland Engdahl