Thanks for the quick replies. I'll try Barton Willis's suggestions and
report back. It may be a few days.
Yes, I do consider success with this approach to be a long shot. After I've
exhausted some possibilities, I'll post a batch file and the underlying
derivation for the scrutiny of those who may have seen this type of problem
before.
Joe Koski
on 4/26/04 11:35 AM, Richard Fateman at fateman@cs.berkeley.edu wrote:
> This error indicates a bug in the polynomial GCD algorithm
> or perhaps in some data transformations leading up to it.
> "Polynomial quotient is not exact" means that the system
> has computed
> G = greatest common divisor of polynomials A and B.
> It then reduces C=A/G, D=B/G.
>
> The error message says that G does not divide A or perhaps B.
>
> What to do?
> Perhaps change the polynomial GCD routine being used.
> Since your problem looks like an elliptic integral, it
> would be surprising if Maxima did it. There is a higher
> probability that the commercial Macsyma, or one of the other M systems
> would do it. So maybe you should post it.
>
> Maxima would consider a problem that required an elliptic function
> to be non-integrable, except perhaps in very rare lucky circumstances.
>
> RJF
>
>
> Joe Koski wrote:
>
>> I'm trying to integrate a function that is a ratio of polynomials in the
>> general form
>>
>> f(x)/g(x)^(3/2)
>>
>> where f(x) and g(x) are relatively complicated polynomials in x. If the
>> integration succeeds, I should have the x-component of the magnetic field
>> (B) for a cubic spline curve segment located in the x-y plane.
>>
>> After many hours, Maxima quits with the error:
>>
>> Polynomial quotient is not exact
>> -- an error. Quitting. To debug this try DEBUGMODE(TRUE);)
>>
>> My questions:
>>
>> 1) Is there a simple explanation of this problem? What is the "polynomial
>> quotient?" All exponents in the polynomials are integers, but their ratios
>> are not, sometimes.
>>
>> 2) Does this indicate that the function can not be integrated at all, or is
>> it a Lisp/Maxima problem?
>>
>> 3) Are there any work-arounds or alternative approaches suggested. There may
>> be some elliptic integrals lurking in the problem, or it could simply be
>> nonintegrable.
>>
>> I've been trying to solve this problem on-and-off for over ten years as a
>> kind of stress test for Maxima and Mathematica. This is the first time the
>> computer has had enough memory and speed to actually give me an error
>> instead of just running out of resources. If this works, I think it could be
>> a useful tool for designing magnet sets, if it doesn't, no harm done.
>>
>> I can post the batch script if it would help. Thanks for any suggestions.
>>
>> Joe Koski
>>
>>
>>
>>
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>>
>>
>