Another integration question



Raymond Toy (RT/EUS) wrote:
> Raymond Toy wrote:
>> 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.
> 
> A bit late perhaps, but...
> 
> It is trying to use residues over the keyhole contour.  Maxima finds the 
> roots of 6*x^4+16*x^3+18*x^2+1.  There are 4 distinct, complex roots. 
> These are very, very messy.  Then you get to find the residues at each 
> of these roots.  I think maxima can actually find the residues, but the 
> expressions are so complex, it takes "forever".  And because they are so 
> complex, I'm not sure maxima will be able to simplify them to something 
> sensible.

I let it run for an hour or two.  Maxima eventually finishes and 
produces some huge expression but the margin was too narrow to hold it.[1]

But if I float the result, I get the expected answer.

Ray

[1]  Well, actually maxima said the expression is too wide to be displayed.