Re: New version, new bugs
- To: mathgroup at smc.vnet.net
- Subject: [mg42397] Re: New version, new bugs
- From: Maxim <dontsendhere@.>
- Date: Fri, 4 Jul 2003 01:33:14 -0400 (EDT)
- References: <be10b9$2l2$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Andrzej Kozlowski wrote: > On Wednesday, July 2, 2003, at 07:36 pm, Maxim wrote: > > > 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); > > My Mathematica 5.0 simply gives: > > Integrate::gener: Unable to check convergence. > > as output to this. Am I missing something? > I was just looking at the Mathworld page; one of the examples there was In[1]= Integrate[Abs[x - y]^n, {x, 0, 1}, {y, 0, 1}] Out[1]= If[Re[n]>-2, 2/((n+1)*(n+2)), Integrate[Abs[x - y]^n, {x, 0, 1}, {y, 0, 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); > > This is true, but > > In[7]:= > Integrate[Log[x], {x, -1, -1 - I}] > > Out[7]= > (-(1/4) + I/4)*((2 - 2*I) + (1 + 2*I)*Pi + 2*I*Log[2]) > > which is correct. > > > > > 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. > > Again, if you use numeric limits Mathematica 5.0 get's it right > > In[8]:= > Integrate[Log[x], {x, I, 1 + I}] > > Out[8]= > (1/4 + I/4)*((-2 + 2*I) + Pi + Log[4]) > > I am not sure that the inability to return always correct answers in > this type of situation when symbolic limits are used is a "bug" rather > than just a limitation of the present system. In any case, the fact > that with numeric limits one gets the right answers is a relief, and > certainly more important in practice. > What's the point of giving the results in the conditional form then? I simply claim that in Integrate[Log[x], {x, a, b}] (again, according to Mathworld) the condition is incorrect. Very cute how the Mathworld page has already been edited.