Yet another abs_integrate trig integral problem

[kcrisman]

See ​this ask.sagemath question. Original report is

sage: F = sqrt((cos(x) - 1)^2 + sin(x)^2)
sage: F.integrate(x, 0, 2*pi)
0

but the answer should be 8.

EDIT: related

sage: F.integrate(x, 0, pi)
4
sage: F.integrate(x, pi, 2*pi)
-4

and the primitive is wrong:

sage: F.integrate(x)
-4/sqrt(sin(x)^2/(cos(x) + 1)^2 + 1)

[kcrisman]

Upstream ​https://sourceforge.net/p/maxima/bugs/2823/

[kcrisman]

See also #12731.

[jakobkroeker]

I suppose, this ticket needs a stopgap?

[kcrisman]

Maybe all the abs_integrate ones do - see #12731. But I don't think it's appropriate to just raise a warning EVERY TIME someone integrates. So there would have to be some way to limit its applicability. I think that is why I never worked on stopgaps; the stuff I was working on doesn't lend itself to easily pointing that out, other than having Sage itself start with a disclaimer "warning: computer math sometimes has errors".

[jakobkroeker]

Sage itself start with a disclaimer "warning: computer math sometimes has errors"

+1

which in additional links to Mathematically Wrong Answers: ​http://trac.sagemath.org/query?status=new&status=needs_work&status=needs_review&status=needs_info&type=defect&stopgaps=!&max=0&order=id

I would support that (to warn the greenhorns), or will that have too much opposition?

but I don't think it's appropriate to just raise a warning EVERY TIME someone integrates.

Agree, so what about showing a stopgap warning only once per user+computer+sageVersion or similar? ( otherwise the user has explicitly request regular stopgap warnings)

[kcrisman]

These are questions above my pay grade, as I did not institute the stopgap system. Again, if there is a way to invoke this when abs_integrate is used, that would be fine - we already have a way to only selectively load packages, but once loaded, I'm not sure we can "unload" it. But continue that discussion at #12731.

[gh-mwageringel]

Possibly related:

sage: integrate(sqrt(1/(2-cos(x))), (x, 0, pi))
0

According to Mathematica, the correct result should be 2*elliptic_kc(-2).

[gh-mwageringel]

See also ​https://groups.google.com/g/sage-devel/c/h50LZVLVQI4.

[chapoton]

The issue with the primitive of F may come from our choice of "domain: complex" in maxima.

Using maxima("domain : real;") gives another answer, that could be better.