doctest fixed integral from Maxima

[kcrisman]

This is fixed now and needs a doctest:

From #sage-devel:

Boulemans left the chat room. (Read error: Connection reset by peer)
[11:58am] Boule joined the chat room.
[11:58am] Boule: (laptop shutdown due to power supply)
[11:59am] Boule: e, T, w = var("e T w"); assume(1 = e^2)>0; integrate(cos(w+T)/(1+e*cos(T))^2,T,0,2*pi) should give -2*pi e cos w/(1-e^2)^3/2 instead of 0
[11:59am] Boule: can someone help?
[12:00pm] wjp: yeah, sage seems to have some trouble with this integral. You could try http://groups.google.com/group/sage-support since the right people don't seem to be here currently
[12:00pm] Boule: ok, thanx
[12:08pm] kcrisman: By the way, I just tried this and get a hang in Maxima.  Can you type the exact commands which lead to an answer of 0?
[12:08pm] kcrisman: If I plug something (.5, .75) in for e in Maxima in Sage, I do get zero as an output.
[12:12pm] Boule: don't know maxima, but with numerical values for e and w at wolfram-alfa, it gives something different than 0
[12:13pm] wjp: *nod* maple gives non-zeros too
[12:13pm] kcrisman: Can you give the *exact* sequence of commands which yield zero in Sage itself? 
[12:14pm] Boule: e = var('e')
[12:14pm] Boule: T = var('T')
[12:14pm] Boule: w = var('w')
[12:14pm] baali1 joined the chat room.
[12:14pm] baali left the chat room. (Quit: Leaving.)
[12:15pm] Boule: assume(1-e^2>0)
[12:15pm] Boule:  integrate(cos(w+T)/(1+e*cos(T))^2,T,0,2*pi)
[12:15pm] kcrisman: Okay, that's what I thought.
[12:16pm] kcrisman: Okay, it takes a while but I do get 0.

Component: calculus

Author: Ralf Stephan

Branch: d4b0db5

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/8728

[jasongrout]

comment:1

I wonder if this is another manifestation of this bug:

sage: integrate(sqrt(sin(x)^2+cos(x)^2), x,0,2*pi)
pi

[jasongrout]

comment:2

#8729 may point to a solution.

[kcrisman]

comment:3

Hmm, I forgot about this, and it's true it never got implemented, did it?

[jasongrout]

comment:4

It was fixed about two weeks ago in maxima. There was a new release of maxima a few days ago---I'm trying to make an spkg right now.

[kcrisman]

comment:5

Sweet. I haven't been keeping up on the Maxima list lately, thanks.

[jasongrout]

comment:6

Replying to @jasongrout:

I wonder if this is another manifestation of this bug:

sage: integrate(sqrt(sin(x)^2+cos(x)^2), x,0,2*pi)
pi

I just checked; this ticket isn't the same bug.

[jasongrout]

comment:7

The upgrade to maxima 5.21.1 does not fix this. After #8731:

sage: e, T, w = var("e T w")    
sage: assume(1-e^2>0)
sage: integrate(cos(w+T)/(1+e*cos(T))^2,T,0,2*pi)                                           
0

[kcrisman]

comment:8

Maxima 5.23.2 still has this, and we still haven't reported it.

Maxima 5.23.2 http://maxima.sourceforge.net
using Lisp SBCL 1.0.24
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) assume(1-e^2>0);
                                     2
(%o1)                              [e  < 1]
(%i3) integrate(cos(w+T)/(1+e*cos(T))^2,T,0,2*%pi);
(%o3)                                  0

This is now Maxima bug 3211975.

[kcrisman]

comment:9

According to the bug report, this is now fixed. However, some examples may still throw a Lisp error, so we should check out whether that will affect us before saying we're totally fixed when we upgrade.

[kcrisman]

Changed upstream from Not yet reported upstream; Will do shortly. to Fixed upstream, but not in a stable release.

[kcrisman]

comment:10

Maxima 5.28 is now out.

[kcrisman]

comment:11

See #13973 where this should (?) be fixed, just need a doctest here?

[pjbruin]

comment:15

In Maxima 5.33.0 (see #13973):

(%i1) assume(e^2<1);
                                     2
(%o1)                              [e  < 1]
(%i2) integrate(cos(w+T)/(1+e*cos(T))^2, T, 0, 2*%pi);
                      2
Is abs(e) - sqrt(1 - e ) - 1 positive, negative or zero?

negative;
   !          2     !
Is !sqrt(1 - e ) - 1! - abs(e) positive, negative or zero?

negative;
                                             2
                           2 %pi e sqrt(1 - e ) cos(w)
(%o2)                    - ---------------------------
                                   4      2
                                  e  - 2 e  + 1

This appears to be the correct answer. Note that the answers to both questions are "negative" for all e with -1 < e < 1, so it would be nice if Maxima didn't ask those questions.

[kcrisman]

comment:17

In Maxima 5.33.0 (see #13973):
This appears to be the correct answer. Note that the answers to both questions are "negative" for all e with -1 < e < 1, so it would be nice if Maxima didn't ask those questions.

The thing noted in the message upstream when they closed their ticket

sage: integrate(cos(w+T)/(1+.5*cos(T))^2,T,0,2*pi)
<boom>

does still happen, but I think that is a different issue tracked elsewhere here (the usual keepfloat thing).

So... do we have a reasonable test case to add here to confirm this is fixed and close it?

[kcrisman]

Changed upstream from Fixed upstream, but not in a stable release. to Fixed upstream, in a later stable release.

[rwst]

comment:19

Here's the doctest:

sage: assume(1-e^2>0)
sage: assume(abs(e)-sqrt(1-e^2)-1>0)
sage: assume(abs(sqrt(1-e^2)-1)-abs(e)>0)
sage: integrate(cos(w+T)/(1+e*cos(T))^2,T,0,2*pi)
2*pi*sqrt(-e^2 + 1)*e*cos(w)/(e^4 - 2*e^2 + 1)

[rwst]

Branch: u/rws/doctest_fixed_integral_from_maxima

[rwst]

Commit: fab7369

[rwst]

New commits:

fab7369

8728: doctest

[rwst]

Author: Ralf Stephan

[pjbruin]

comment:22

Your assumptions are contradictory: the first assumption (1 - e^2 > 0) implies the negation of the other two assumptions (see also comment:15).

A fortiori, the other two assumptions (after negating) are actually redundant. It is annoying that we have to add them; ideally, we would only declare this integral to be "fixed" if Maxima did not need the extra two assumptions...

[rwst]

Changed branch from u/rws/doctest_fixed_integral_from_maxima to u/rws/8728

[rwst]

Changed upstream from Fixed upstream, in a later stable release. to none

[rwst]

Changed commit from fab7369 to d4b0db5

[rwst]

New commits:

d4b0db5

8728: doctest fixed integral from Maxima

[tscrim]

Reviewer: Travis Scrimshaw

[vbraun]

Changed branch from u/rws/8728 to d4b0db5

[pjbruin]

Changed commit from d4b0db5 to none

[pjbruin]

comment:27

I noticed just now that this ticket has been closed; it seems comment:15 and comment:22 were ignored...

[rwst]

comment:28

That would seem so. I think you are asking for a feature (redundancy of additional assumptions) in Maxima that would warrant a separate ticket. I apologize for not answering earlier.

[pjbruin]

comment:29

Replying to @rwst:

I think you are asking for a feature (redundancy of additional assumptions) in Maxima that would warrant a separate ticket.

That too, but more importantly I meant the fact that the assumptions that are currently made in the doctest are mutually inconsistent:

assume(1-c^2 > 0)
assume(abs(c) - sqrt(1-c^2) - 1 > 0)
assume(abs(sqrt(1-c^2)-1) - abs(c) > 0)

Namely, the first assumption is equivalent to -1 < c < 1, and on this domain the functions abs(c) - sqrt(1-c^2) - 1 and abs(sqrt(1-c^2)-1) - abs(c) are strictly negative.

There is already some functionality for detecting inconsistent assumptions (e.g. assume(x > 0); assume(x < 0) raises an error), but it doesn't detect this case.