#8728: doctest fixed integral from Maxima
-------------------------------------------------+-------------------------
Reporter: kcrisman | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: calculus | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: Fixed upstream, in a later | Work issues:
stable release. | Commit:
Branch: | Stopgaps:
Dependencies: |
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Old description:
> 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.
> }}}
New description:
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.
}}}
--
Comment (by rws):
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)
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/8728#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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