#3661 calculates geometric sum incorrectly inside integrate function

[osman buyukisik]

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Maxima version: "5.43.0"
Maxima build date: "2019-08-28 00:34:58"
Host type: "x86_64-unknown-linux-gnu"
Lisp implementation type: "GNU Common Lisp (GCL)"
Lisp implementation version: "GCL 2.6.12"
User dir: "/home/carol/.maxima"
Temp dir: "/tmp"
Object dir: "/home/carol/.maxima/binary/5_43_0/gcl/GCL_2_6_12"
Frontend: false

---

simpsum is false by default.
Maxima 5.43.0 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.12
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d:false;

(%o1) false
(%i2) integrate(x^(sum(1/2^k,k,1,inf)),x);
Is 'sum(1/2^k,k,1,inf) equal to -1?

no;
(%o2) x^('sum(1/2^k,k,1,inf)+1)/('sum(1/2^k,k,1,inf)+1)

This is correct but not in the desired form. simpsum:true prior to invokation results in the correct form.
why does it think the sum might be -1? Why ask the user for that simple sum anyways?
Same result for SBCL based maxima too.

[Robert Dodier]

I'm not sure what to think of this. integrate is asking about -1 since if the exponent is -1 it will return a logarithm. Figuring out that the sum is easily calculated isn't really obvious within integrate, and I'm not sure we would want to try all the heuristics known to Maxima (which are collected in the simplify_sum package).

I'm leaning towards thinking that this is a case where it's reasonable to expect the user to help out, by calling simplify_sum for example. If anyone else has an opinion I'll be glad to hear it.

[David Billinghurst]

I also think it is reasonable to expect the user to help out here.

[Robert Dodier]

I've marked this as "not a bug". Osman, thanks for your interest in Maxima and taking the time to submit a ticket.