MaplePrimes - comments on Post, What is padic?

MaplePrimes - comments on Post, What is padic? http://www.mapleprimes.com/posts/125644-What-Is-Padic en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Fri, 12 Jun 2026 13:10:49 GMT Fri, 12 Jun 2026 13:10:49 GMT The latest comments added to the Post, What is padic? http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, What is padic? http://www.mapleprimes.com/posts/125644-What-Is-Padic number theory http://www.mapleprimes.com/posts/125644-What-Is-Padic?ref=Feed:MaplePrimes:What is padic?:Comments#comment125681 Number Theory It is decades ago, so a vague answer. And please do not take it as one to look sooo much educated, it is just since nobody else takes the question. The guys in Number Theory use it in arithmetics Geometry, making heavy use of cohomology theories (plural) in translating problems. One should find more around "Weil Conjecture" on Wikipedia. Or Serre's book on Falting's proof (in the bookshelf, section "I should ... but later or never ..."). Never made up my mind to 'learn' it seriously, it is a tough machine ... Being ignorant I hesitate to say more. The latest comments added to the Post, What is padic? 125681 Thu, 15 Sep 2011 23:45:31 Z Axel Vogt Axel Vogt p-adics http://www.mapleprimes.com/posts/125644-What-Is-Padic?ref=Feed:MaplePrimes:What is padic?:Comments#comment126355 Not being a number theorist, I haven't made much use of p-adics.  However, the p-adic order of a rational number is something that is often quite handy, and padic[ordp] will compute it.  Thus if p is a prime and  r is a nonzero rational number, padic[ordp](r, p) will compute the integer n such that r = pna/b where a and b are integers coprime to p. Another command in the padic package is rootp, which finds p-adic roots of a polynomial in one variable.  How might this be helpful to a non-specialist?  Well, it can be thought of as encoding information about the solutions of this polynomial modulo different powers of p.  For example: > padic[rootp](x^3+x+3,13); <img src="data:image/png;base64,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" alt=""> So x=9 is a solution of x3+x+3 = 0 mod 13, and x=9 + 6 . 13 = 87 is a solution of this equation mod 132, etc.: since (if rootp can be believed) there is a 13-adic root of the polynomial. the truncations of that root give solutions mod 13n for each positive integer n.  There happens to be another solution of x3+x+3 = 0 mod 13, namely x = 2, but that one doesn't "lift" to the next power of 13. The latest comments added to the Post, What is padic? 126355 Sat, 08 Oct 2011 03:18:53 Z Robert Israel Robert Israel Applications http://www.mapleprimes.com/posts/125644-What-Is-Padic?ref=Feed:MaplePrimes:What is padic?:Comments#comment129132 The  applications of p-adic numbers outside of  number theory and  algebra are discussed here: <a href="http://mathoverflow.net/questions/84320/important-applications-of-p-adic-numbers-outside-of-algebra-and-number-theory">http://mathoverflow.net/questions/84320/important-applications-of-p-adic-numbers-outside-of-algebra-and-number-theory</a> The latest comments added to the Post, What is padic? 129132 Tue, 27 Dec 2011 10:46:29 Z Markiyan Hirnyk Markiyan Hirnyk What is the p-adic Mandelbroit set? http://www.mapleprimes.com/posts/125644-What-Is-Padic?ref=Feed:MaplePrimes:What is padic?:Comments#comment151041 I would like to pay attention to  the recent notice <a href="http://www.ams.org/notices/201308/rnoti-p1048.pdf">http://www.ams.org/notices/201308/rnoti-p1048.pdf</a> . The latest comments added to the Post, What is padic? 151041 Wed, 28 Aug 2013 16:53:33 Z Markiyan Hirnyk Markiyan Hirnyk