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#1353 taylor message about something assumed to be 0 in integral
Dear Developers of Maxima,
I found that a simple integration about trigonometric functions yields
some strange message as follows:
\-------------------------------------------------------------------------------
\[wisdom3:~/work/280:1\] adachi% cat message\_assumed\_to\_be\_zero\_in\_taylor\_from\_simple\_integrations.maxima
integrate\(\(1+cos\(t\)\)^5,t,0,2\*%pi\);
\[wisdom3:~/work/280:2\] adachi% maxima -b message\_assumed\_to\_be\_zero\_in\_taylor\_from\_simple\_integrations.maxima
Maxima 5.14.0cvs http://maxima.sourceforge.net
Using Lisp GNU Common Lisp \(GCL\) GCL 2.6.7 \(aka GCL\)
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.
\(%i1\)
batch\(message\_assumed\_to\_be\_zero\_in\_taylor\_from\_simple\_integrations.maxima\)
batching \#p/Volumes/HFS+2/home/adachi/work/280/message\_assumed\_to\_be\_zero\_in\_taylor\_from\_simple\_integrations.maxima
5
\(%i2\) integrate\(\(cos\(t\) + 1\) , t, 0, 2 %pi\)
9
yy
Assumed to be zero in \`taylor'
9
yy
Assumed to be zero in \`taylor'
63 %pi
\(%o2\) ------
4
\-------------------------------------------------------------------------------
The result of calculation is correct. But the strange message
"yy^9 Assumed to be zero in `taylor'" is printed twice.
This message is at least useless for end users.
Please fix the routine for the above integration.
Thank you very much for developing Maxima.
Sincerely yours
Satoshi Adachi
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FWIW, maxima eventually calls intsc1 to evaluate this integral. This in turn eventually calls zto%pi2, which uses residues inside the unit circle to compute this integral. Scrat convert the exponentializes the integrand and also changes the variable of integration to yy.
I guess the computation of the residues (via RES) uses Taylor series.
Note that if the exponent is changed from 5 to 4, the warning isn't given.
I do not know why taylor produces the warning.
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Not sure what we can do about this. We can suppress the message, I guess, but it probably represents a proviso or restriction on an intermediate result, which, ideally, would be carried through to the final result. I guess taylor and integrate share responsibility here; taylor doesn't construct a proviso object of any kind, and integrate probably isn't equipped to handle such a thing anyway.
Because of revision 1.43 of hayat.lisp and revision 1.14 of residu.lisp the reported problem is no longer present. We get:
(%i3) integrate((cos(t) + 1)^5 , t, 0, 2*%pi);
(%o3) 63*%pi/4
Closing this bug report as fixed.
Dieter Kaiser