New version, new bugs
- To: mathgroup at smc.vnet.net
- Subject: [mg42365] New version, new bugs
- From: Maxim <dontsendhere@.>
- Date: Wed, 2 Jul 2003 06:36:27 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Funny that it is easy to find errors even in a couple of demonstrational examples of Mathematica's new capabilities on the Mathworld page (http://mathworld.wolfram.com/news/2003-06-23/mathematica5/): 1) Re[n]>-2 is not a correct convergence condition for Integrate[Abs[x - y]^n, {x, 0, 1}, {y, 0, 1}] (a quick way to see that there's something wrong is to look at the sign of Mathematica's answer when -2<n<-1); 2) Integrate[Log[x], {x, a, b}]/.{a->-1,b->-1-I} gives incorrect answer I + I*Pi - (1 + I)*Log[-1 - I]; this is the tricky case when one of the *endpoints* of the integration path is on the branch cut (see http://library.wolfram.com/infocenter/MathSource/4741/, where this situation is considered for rational functions); 3) Integrate[Log[x], {x, a, b}]/.{a->I,b->1+I} gives Power::infy: Infinite expression 1/0 encountered. Greater::nord: Invalid comparison with ComplexInfinity attempted. Power::infy: Infinite expression 1/0 encountered. Greater::nord: Invalid comparison with ComplexInfinity attempted. Out[1]= If[ComplexInfinity >= 0 || ComplexInfinity >= 0, <<1>>] because conditions describing the position of the integration path that doesn't cross the branch cut do not include the possibility of the two being parallel. Maxim Rytin m.r at prontomail.com