internal function of fricas appearing

[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.

[mantepse]

New commits:

​f18b821	add doctest
​0bf981c	provide doctest

[chapoton]

First one does not work for me on 9.4.b0. We must wait for Fricas release containing the fix.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​322dfb7

Merge branch 'develop' into t/28630/wrong_conversion_from_fricas

[dimpase]

this gives me

File "src/sage/symbolic/integration/external.py", line 418, in sage.symbolic.integration.external.fricas_integrator
Failed example:
    integrate(f, x, algorithm="fricas")                               # optional - fricas
Expected:
    1/315*(64512*I*a*e^(10*I*d*x + 10*I*c) + 53760*I*a*e^(8*I*d*x + 8*I*c) + 30720*I*a*e^(6*I*d*x + 6*I*c) + 11520*I*a*e^(4*I*d*x + 4*I*c) + 2560*I*a*e^(2*I*d*x + 2*I*c) + 256*I*a)/(d*e^(20*I*d*x + 20*I*c) + 10*d*e^(18*I*d*x + 18*I*c) + 45*d*e^(16*I*d*x + 16*I*c) + 120*d*e^(14*I*d*x + 14*I*c) + 210*d*e^(12*I*d*x + 12*I*c) + 252*d*e^(10*I*d*x + 10*I*c) + 210*d*e^(8*I*d*x + 8*I*c) + 120*d*e^(6*I*d*x + 6*I*c) + 45*d*e^(4*I*d*x + 4*I*c) + 10*d*e^(2*I*d*x + 2*I*c) + d)
Got:
    -256/315*(-252*I*a*e^(10*I*d*x + 10*I*c) - 210*I*a*e^(8*I*d*x + 8*I*c) - 120*I*a*e^(6*I*d*x + 6*I*c) - 45*I*a*e^(4*I*d*x + 4*I*c) - 10*I*a*e^(2*I*d*x + 2*I*c) - I*a)/(d*e^(20*I*d*x + 20*I*c) + 10*d*e^(18*I*d*x + 18*I*c) + 45*d*e^(16*I*d*x + 16*I*c) + 120*d*e^(14*I*d*x + 14*I*c) + 210*d*e^(12*I*d*x + 12*I*c) + 252*d*e^(10*I*d*x + 10*I*c) + 210*d*e^(8*I*d*x + 8*I*c) + 120*d*e^(6*I*d*x + 6*I*c) + 45*d*e^(4*I*d*x + 4*I*c) + 10*d*e^(2*I*d*x + 2*I*c) + d)

• a different formatting of the same expression.

[dimpase]

how about making this doctest robust:

        sage: ii=integrate(f, x, algorithm="fricas")                    # optional - fricas
        sage: ii==1/315*(64512*I*a*e^(10*I*d*x + 10*I*c) +<the rest...> # optional - fricas
        True

[dimpase]

OK, like this

---

New commits:

​4f3e1b4

make the test robust

[mantepse]

The final commit subsumes #29043, which I therefore set to duplicate.