tag:blogger.com,1999:blog-3360583082244632912.post3698258238691368115..comments2016-11-10T20:58:27.670+01:00Comments on Misha Lemeshko's blog: A bug in Mathematica - 6 years laterMikhail Lemeshkohttps://plus.google.com/103756143785392236413noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-3360583082244632912.post-3542910547340058452016-04-20T10:56:14.789+02:002016-04-20T10:56:14.789+02:00Sorry, there should be Abs[] of the sum of exponen...Sorry, there should be Abs[] of the sum of exponent. And Mathematica gives 0 for this integral, which is incorrect. I will send you the article so that you could try the example by yourself.Rytis Jursenashttp://www.blogger.com/profile/15140168476438921311noreply@blogger.comtag:blogger.com,1999:blog-3360583082244632912.post-38506852955768176162016-04-20T10:43:53.235+02:002016-04-20T10:43:53.235+02:00Yes, please email it to me!
If you mean NIntegrat...Yes, please email it to me!<br /><br />If you mean NIntegrate[NIntegrate[Exp[2*Pi*I*x] + Exp[2*Pi*I*y], {x, 0, 1}], {y, 0, 1}] (I erased an extra "]"), it indeed gives a complex number, but the imaginary part disappears if one cranks up WorkingPrecision.<br /><br />MishaMikhail Lemeshkohttp://www.blogger.com/profile/10683436629380140783noreply@blogger.comtag:blogger.com,1999:blog-3360583082244632912.post-27051812979016687712016-04-20T10:40:37.305+02:002016-04-20T10:40:37.305+02:00Maybe that's because it was 9.0.1 version. Wha...Maybe that's because it was 9.0.1 version. What about NIntegrate[NIntegrate[Exp[2*Pi*I*x]+Exp[2*Pi*I*y]],{x,0,1}],{y,0,1}] ? In any case, if you want I can email you that article.Rytis Jursenashttp://www.blogger.com/profile/15140168476438921311noreply@blogger.comtag:blogger.com,1999:blog-3360583082244632912.post-39096193377977268932016-04-20T10:33:03.549+02:002016-04-20T10:33:03.549+02:00Thanks, Rytis! This is funny, my mathematica's...Thanks, Rytis! This is funny, my mathematica's output is 7.847 for this integral...<br /><br />MishaMikhail Lemeshkohttp://www.blogger.com/profile/10683436629380140783noreply@blogger.comtag:blogger.com,1999:blog-3360583082244632912.post-27516273432722137392016-04-20T10:28:38.956+02:002016-04-20T10:28:38.956+02:00Hi, just wanted to remark that there is an article...Hi, just wanted to remark that there is an article in AMS Notices, November 2014 issue, that discusses if one can trust computer algebra systems and in particular Mathematica. Another example given there: Integrate[Sqrt[(2t)^2+(4-3t^2)^2],{t,0,2}]//N gives the complex number 0.881679+1.17073i, although in reality the integrand (2t)^2+(4-3t^{2})^{2}>0 is a positive number for 0<=t<=2. Best from Rytis.Rytis Jursenashttp://www.blogger.com/profile/15140168476438921311noreply@blogger.com