Re: Magic number 23
- To: mathgroup at smc.vnet.net
- Subject: [mg41491] Re: Magic number 23
- From: bobhanlon at aol.com (Bob Hanlon)
- Date: Thu, 22 May 2003 06:57:21 -0400 (EDT)
- References: <bafq4t$6qk$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
To force evaluation of Sin[Pi/8] and similar values use FunctionExpand. To see why some values are very time consuming look at Sin[Pi/11]//FunctionExpand FullSimplify is very slow when working with these large expressions. Bob Hanlon In article <bafq4t$6qk$1 at smc.vnet.net>, "Ingolf Dahl" <ingolf.dahl at telia.com> wrote: << Subject: RE: Magic number 23 From: "Ingolf Dahl" <ingolf.dahl at telia.com> To: mathgroup at smc.vnet.net Date: Wed, 21 May 2003 12:06:53 +0000 (UTC) I did not specify exactly what I meant by "exact value", and of course one could consider Sin[Pi/23] to be an "exact value" by itself. But what I meant was an expression involving integers and radicals. If we allow Root expressions, the question about the number of exact values becomes almost trivial. Maybe the operation ToRadicals should be redefined to also convert expressions of this type. I find it a bit surprising that Mathematica does not give radical expressions for Sin[Pi/8] and Cos[Pi/8]. These were given in my school math tables. One (recreational) use of these expressions are to find different ways to express Pi. If we know an exact expression of Tan[Pi/12], for instance, we might use this value as x, and use the power expansion of ArcTan[x] to obtain a series with the sum Pi/12. And if we use Tan[Pi/2^20] in the same way, we should obtain a commplicated expression, but a very rapid convergence. But, still, what is so special with Sin[Pi/23]? What is FullSimplify trying to do with it? And why do some other primes take so long to evaluate? FullSimplify does not succeed to do anything with these expressions, it just is wasting time. On a second run of the evaluations with the same Kernel, FullSimplify has learnt the lesson, and the evaluations are immediate. Ingolf Dahl Sweden >><BR><BR>