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)

Upstream: Fixed upstream, but not in a stable release.

Component: calculus

Keywords: abs_integrate

Stopgaps: #12731

Issue created by migration from https://trac.sagemath.org/ticket/17183

[kcrisman]

Changed upstream from Not yet reported upstream; Will do shortly. to Reported upstream. No feedback yet.

[kcrisman]

comment:1

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

[kcrisman]

Description changed:

--- 
+++ 
@@ -1,6 +1,8 @@
 See [this ask.sagemath question](http://ask.sagemath.org/question/24532/).  Original report is 
 
 ```
-F = sqrt((cos(x) - 1)^2 + sin(x)^2)
-F.integrate(x, 0, 2*pi)
+sage: F = sqrt((cos(x) - 1)^2 + sin(x)^2)
+sage: F.integrate(x, 0, 2*pi)
+0
 ```
+but the answer should be 8.

[kcrisman]

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

[kcrisman]

comment:3

See also #12731.

[sagetrac-jakobkroeker]

Stopgaps: todo

[sagetrac-jakobkroeker]

comment:5

I suppose, this ticket needs a stopgap?

[kcrisman]

comment:6

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".

[sagetrac-jakobkroeker]

comment:7

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]

comment:8

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.

[sagetrac-jakobkroeker]

Changed stopgaps from todo to #12731