Barton Willis wrote:
> -----maxima-bounces at math.utexas.edu wrote: -----
>
>> To: maxima at math.utexas.edu
>> From: max.e.brown at gmail.com
>> Sent by: maxima-bounces at math.utexas.edu
>> Date: 08/21/2007 08:19AM
>> Subject: Another integration question
>>
>> I stumbled across a definite integral that seems to make Maxima
>> hang. Has anyone seen this before?
>>
>> -8<------------
>> (%i1) integrate( (x^3+1)/(x^4 + 4*x + 1), x);
>> 4
>> log(x + 4 x + 1)
>> (%o1) -----------------
>> 4
>> (%i2) integrate( (x^3+1)/(x^4 + 4*x + 1), x, 0, 1);
>>
>> [... no output, sblc cpu usage at 87% ...]
>
> I don't know what happens if you don't stop Maxima, but
> I think you should file a bug report.
>
> To see in part what is going on, try this:
>
> (%i4) trace(?csign);
> (%o4) [csign]
> (%i5) integrate( (x^3+1)/(x^4 + 4*x + 1), x, 0, 1);
>
> --> Yikes! all kinds of junk!
>
Neat.
I'm not exactly sure what's going on, but when I stopped it, the
backtrace said it was trying to use contour integration of
(6*x^3+12*x^2+9*x+2)*plog(-x)/(6*x^4+16*x^3+18*x^2+8*x+1)
over the keyhole contour (a circle with a slit on the positive real
axis). And plog is the principal log function.
I don't know if this is where it gets stuck in a loop or if this method
fails and another is attempted.
Ray