[Maxima-bugs] [ maxima-Bugs-2890315 ] integrate(cot(x)^4, x, %pi/6, %pi/2) answer

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Bugs item #2890315, was opened at 2009-11-01 16:54
Message generated for change (Comment added) made by crategus
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Category: Lisp Core - Integration
Group: None
>Status: Open
>Resolution: None
Priority: 5
Private: No
Submitted By: mitreuden (mitreude)
Assigned to: Nobody/Anonymous (nobody)
Summary: integrate(cot(x)^4,x,%pi/6,%pi/2) answer

Initial Comment:
The first time integrate(cot(x)^4,x,%pi/6,%pi/2) is executed, the answer of %pi/3 returned is correct.  However, when the integral is computed again, an incorrect answer of 4*%pi/3 is returned.

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>Comment By: Dieter Kaiser (crategus)
Date: 2009-11-03 23:21

Message:
I can see this bug too with CLISP 2.44 and Maxima 5.19post on my Linux
system:

(%i2)  integrate(cot(x)^4,x,%pi/6,%pi/2);
(%o2) %pi/3
(%i3)  integrate(cot(x)^4,x,%pi/6,%pi/2);
(%o3) 4*%pi/3

Evaluating this integral the package trgsmp is loaded:

(%i5) functions;
(%o5) [trigonometricp(exp),trigsimp(x),trigsimp3(expn),trigsimp1(expn),
       improve(expn,subsofar,listoftrigsq),listoftrigsq(expn),
      
specialunion(list1,list2),update(form,complement),expnlength(expr),
       argslength(args)]

When I kill the functions defined by this package the integral is correct
again:

(%i6) kill(functions);
(%o6) done
(%i7)  integrate(cot(x)^4,x,%pi/6,%pi/2);
(%o7) %pi/3

And the next evaluation is wrong again:

(%i8)  integrate(cot(x)^4,x,%pi/6,%pi/2);
(%o8) 4*%pi/3

When I preload the package trgsmp I get the error immediately:

(%i11) kill(functions);
(%o11) done
(%i12) load(trgsmp);
(%o12) "/usr/local/share/maxima/5.19post/share/trigonometry/trgsmp.mac"
(%i13)  integrate(cot(x)^4,x,%pi/6,%pi/2);
(%o13) 4*%pi/3

Reopening the bug report.

Dieter Kaiser

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Comment By: Raymond Toy (rtoy)
Date: 2009-11-02 17:25

Message:
Neat bug.  But current cvs returns %pi/3 both times.

Do not know what has changed, but it seems current CVS has fixed this
issue.

Marking as pending/worksforme

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Comment By: mitreuden (mitreude)
Date: 2009-11-02 04:46

Message:
This problem occurs with version 5.19.2 of Maxima.

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