Re: Different answer when running cell second time?

*To*: mathgroup at smc.vnet.net*Subject*: [mg109715] Re: Different answer when running cell second time?*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Thu, 13 May 2010 07:24:48 -0400 (EDT)

On 5/12/10 at 7:33 AM, jason.lee.quinn at gmail.com (Jason Quinn) wrote: >If I open Mathematica 7.01.0 (64-bit Linux version) that only >contains the following input in a single cell, >Assuming[\[Sigma] > 0, Integrate[p/((Pi*\[Sigma]^2)*E^((p^2 - >2*p*p0*Cos[2*(\[Phi] - \[Phi]0)] + p0^2)/(2*\[Sigma]^2))), {p0, 0, >Infinity}]] >When I hit shift-enter, I get an answer. If I hit, shift-enter a >second time, I get a different answer. Can anybody tell me why? This >seems like a bug. It happens even if I clear all the variables used >in the calculation. I get the same results using Mathematica 7.01 on Mac OS X. The two results look to be equivalent with the second result being simpler than the first. When Integrate does its thing, it caches intermediate results. The first time you execute Integrate, it returns an answer likely based on the first solution found and time constraints built into the algorithms Integrate uses. But the second time you execute Integrate, the intermediate results are still available in a cache. These intermediate results allow further simplification within whatever constraints are built into Integrate.