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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