Re: Inconsistent behaviour of Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg112516] Re: Inconsistent behaviour of Integrate
- From: Bill Rowe <readnews at sbcglobal.net>
- Date: Sat, 18 Sep 2010 07:25:28 -0400 (EDT)
On 9/17/10 at 6:40 AM, andimai at web.de (Andreas Maier) wrote: >On Sep 15, 10:39 am, Bill Rowe <readn... at sbcglobal.net> wrote: >>But given the time it requires to evaluate the integral, why do it >>twice if you get an acceptable answer the first time? >Call me conservative, but I expected to get the same result, when >I'm doing the same calculation again. So I thought, this could be a >bug in Mathematica and I gave the simplest example, where I >encountered this "bug". Ignoring code that makes use of Random and its kin or code using machine precision arithmetic, as far as I am aware, Mathematica always returns the same result given the same input for a given machine/system. But the key here is starting at the same place each time. And that means you need to be aware Mathematica caches intermediate results and clear this cache to obtain the same starting conditions. In fact, it probably isn't necessary to exclude machine precision arithmetic or code that makes use of Random etc., to make the statement Mathematica gives repeatable results with the same starting condition. But it is necessary to realize simply re-executing Mathematica code isn't sufficient to ensure the same starting conditions. The way to check a given result in Mathematica is not to simply repeat execution of the code that gave you the result you are trying to check. Instead, you need to look at other ways of getting the same result or verifying the result satisfies known criteria for valid results.