Different answer when running cell second time?
in [Mathematica]
|
Prev: Cardinality Constraints in quadratic optimization
Next: Trying to remove item from list of filenames
From: Jason Quinn on 12 May 2010 07:33 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. Jason PS This version of Mathematica on Linux has been extremely buggy for me. Abort and Interrupt do not work properly. Mathematica crashes very frequently and seems to revert my documents back to the state they when when I opened Mathematica even if I have saved in the mean time. Palletes and other floating popups do not function properly with the window manager on Ubuntu and sometimes have no title bar or other means to move them around. PPS The two answers are (E^(-((p^2 Sin[2 \[Phi] - 2 \[Phi]0]^2)/( 2 \[Sigma]^2))) p (Sqrt[p^2 Cos[2 \[Phi] - 2 \[Phi]0]^2] + p Cos[2 \[Phi] - 2 \[Phi]0] Erf[Sqrt[( p^2 Cos[2 \[Phi] - 2 \[Phi]0]^2)/\[Sigma]^2]/Sqrt[ 2]]))/(Sqrt[\[Pi]] \[Sigma] Sqrt[ p^2 (1 + Cos[4 \[Phi] - 4 \[Phi]0])]) and (E^(-((p^2 Sin[2 \[Phi] - 2 \[Phi]0]^2)/( 2 \[Sigma]^2))) p (1 + Erf[(p Cos[2 \[Phi] - 2 \[Phi]0])/(Sqrt[2] \[Sigma])]))/(Sqrt[ 2 \[Pi]] \[Sigma])
From: Bill Rowe on 13 May 2010 07:24 On 5/12/10 at 7:33 AM, jason.lee.quinn(a)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.
From: Nasser M. Abbasi on 18 May 2010 06:12
"Jason Quinn" <jason.lee.quinn(a)gmail.com> wrote in message news:hse3lp$34s$1(a)smc.vnet.net... > 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. > > Jason > > PS This version of Mathematica on Linux has been extremely buggy for > me. Abort and Interrupt do not work properly. Mathematica crashes very > frequently and seems to revert my documents back to the state they > when when I opened Mathematica even if I have saved in the mean time. > Palletes and other floating popups do not function properly with the > window manager on Ubuntu and sometimes have no title bar or other > means to move them around. > > PPS The two answers are > > (E^(-((p^2 Sin[2 \[Phi] - 2 \[Phi]0]^2)/( > 2 \[Sigma]^2))) p (Sqrt[p^2 Cos[2 \[Phi] - 2 \[Phi]0]^2] + > p Cos[2 \[Phi] - 2 \[Phi]0] Erf[Sqrt[( > p^2 Cos[2 \[Phi] - 2 \[Phi]0]^2)/\[Sigma]^2]/Sqrt[ > 2]]))/(Sqrt[\[Pi]] \[Sigma] Sqrt[ > p^2 (1 + Cos[4 \[Phi] - 4 \[Phi]0])]) > > > > and > > > (E^(-((p^2 Sin[2 \[Phi] - 2 \[Phi]0]^2)/( > 2 \[Sigma]^2))) p (1 + > Erf[(p Cos[2 \[Phi] - 2 \[Phi]0])/(Sqrt[2] \[Sigma])]))/(Sqrt[ > 2 \[Pi]] \[Sigma]) > > I get the same behavior on windows 7 XP2, using M7 But the good thing is that, both results are correct, as can be seen by using FullSimplify: Assuming[\[Sigma] > 0, FullSimplify[ Integrate[p/((Pi*\[Sigma]^2)*E^((p^2 - 2*p*p0*Cos[2*(\[Phi] - \[Phi]0)] + p0^2)/(2*\[Sigma]^2))), {p0, 0, Infinity}]]] You will now get the second, shorter looking result. My guess of what happens is this: When you first run the command, some internal package gets loaded, but it is loaded in some order by which its effect does not show up yet. When you run the command again, now this package is loaded, and its effect shown up. The effect is just more simplification is done on the expression. --Nasser |