internal function of fricas appearing

[sagetrac-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

Depends on #32049

CC: @hemmecke @sagetrac-whuss @rwst @fchapoton @mantepse

Component: symbolics

Keywords: FriCAS

Author: Martin Rubey

Branch/Commit: 4f3e1b4

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/28630

[fchapoton]

Changed keywords from none to FriCAS

[fchapoton]

comment:4

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]

comment:5

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]

comment:6

I reported this at

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

[mantepse]

Upstream: Reported upstream. No feedback yet.

[mantepse]

Changed upstream from Reported upstream. No feedback yet. to Reported upstream. Developers acknowledge bug.

[embray]

comment:8

Ticket retargeted after milestone closed

[mkoeppe]

comment:9

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

[mkoeppe]

comment:10

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