# [Maxima] Quotient by poly... From definite integration

Barton Willis willisb at unk.edu
Fri Jul 6 12:16:04 CDT 2007

```In Maxima 5.12, gcd defaults to spmod; using the default for gcd, we have

(%i1) k : (1+z^2)^4/ (1+z^4)^4\$
(%i2) gcd : spmod\$

This is wrong:

(%i3) integrate (k,z,0,inf);
(%o3) 0

(%i4) quad_qagi (k, z, 0, inf);
(%o4) [1.770211170672474,2.1230345250168963*10^-11,165,0]

Integrating each term of the partial fraction decomposition of k
seems to give the correct value:

(%i5) map(lambda([e],integrate(e,z,0,inf)), partfrac(k,z));
(%o5) (51*sqrt(2)*%pi)/128

(%i6) float(%);
(%o6) 1.770211170672474

Barton

-----maxima-bounces at math.utexas.edu wrote: -----

>To: "'maxima list'"
>From: "Richard Fateman"
>Sent by: maxima-bounces at math.utexas.edu
>Date: 07/06/2007 11:42AM
>Subject: [Maxima] Quotient by poly... From definite integration
>
> in wxmaxima 0.7.1
>K: (1+z^2)^4/ (1+z^4)^4
>
>integrate (k,z,0,inf);
>Quotient by a polynomial of higher degree -- an error.  To debug this try
>debugmode(true);
>
>[that's with gcd:subres]
>
>--> 0 with gcd:ez
>
>[with gcd:mod]
>-->  goes on forever.
>
>
>_______________________________________________
>Maxima mailing list
>Maxima at math.utexas.edu
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```