Wrong conversion from fricas

[tmonteil]

As reported on ​this ask question, we have:

sage: f = polylog(3, x)
sage: f.integral(x, algorithm='fricas')
-x*%iint(x, -log(-x + 1)/x) - (x - 1)*log(-x + 1) + x*polylog(3, x) + x

So, fricas produces something that is ill-interpreted as some %iint symbolic function.

Note that maxima produces the following answer:

sage: f.integral(x, algorithm='maxima')
-x*dilog(x) - (x - 1)*log(-x + 1) + x*polylog(3, x) + x

[chapoton]

This seems to be some kind of bug in Fricas:

sage: f = fricas(polylog(3,x))
sage: f.integrate(x)
              log(- x + 1)
- x %iint(x,- ------------) + x polylog(3,x) + (- x + 1)log(- x + 1) + x
                    x

And the first term can be differentiated (inside Fricas) correctly.

[mantepse]

More a reminder to myself: SageMath's dilog(x) is FriCAS' dilog(1-x). This is properly reflected in sage.functions.log.py, in class Function_dilog.

So FriCAS should simplify %iint(x, -log(1-x)/x)) to FriCAS dilog(1-x).

[mantepse]

I reported this at

​https://groups.google.com/forum/#!topic/fricas-devel/olmzqJ6IJsE

[embray]

Ticket retargeted after milestone closed

[mkoeppe]

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

[mkoeppe]

Still the same in 9.2.beta10 after the update of FriCAS to 1.3.6 in #27309

[dimpase]

Fricas devs say that %iint should have never appeared, it's a Fricas ​bug. So that's something for them to fix.

[mkoeppe]

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review.