incorrect integration

[rtoy]

Imported from SourceForge on 2024-07-09 19:34:28
Created by kcrisman on 2021-06-07 14:24:45
Original: https://sourceforge.net/p/maxima/bugs/3795

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The following integration does not seem to be correct. Plotting the last entry a-h should give the zero function, but instead is something wavy.

Maxima 5.42.2 http://maxima.sourceforge.net
using Lisp ECL 16.1.2
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) display2d: false;

(%o1) false
(%i2) a: sin((x-y)/sqrt(2))*(x-y);     

(%o2) sin((x-y)/sqrt(2))*(x-y)
(%i3)  g: integrate(a,y);  

(%o3) ((2^(3/2)+2)*sin(y/sqrt(2)-x/sqrt(2))
 +(((-2^(3/2))-2)*(y/sqrt(2)-x/sqrt(2))+((-sqrt(2))-2)*x)
  *cos(y/sqrt(2)-x/sqrt(2)))
 /2
 +sqrt(2)*x*cos(y/sqrt(2)-x/sqrt(2))
(%i4) h: diff(g,y);                             

(%o4) ((-((((-2^(3/2))-2)*(y/sqrt(2)-x/sqrt(2))+((-sqrt(2))-2)*x)
 *sin(y/sqrt(2)-x/sqrt(2)))
 /sqrt(2))
 +((2^(3/2)+2)*cos(y/sqrt(2)-x/sqrt(2)))/sqrt(2)
 +(((-2^(3/2))-2)*cos(y/sqrt(2)-x/sqrt(2)))/sqrt(2))
 /2
 -x*sin(y/sqrt(2)-x/sqrt(2))
(%i5) a-h;

(%o5) (-((-((((-2^(3/2))-2)*(y/sqrt(2)-x/sqrt(2))+((-sqrt(2))-2)*x)
 *sin(y/sqrt(2)-x/sqrt(2)))
 /sqrt(2))
 +((2^(3/2)+2)*cos(y/sqrt(2)-x/sqrt(2)))/sqrt(2)
 +(((-2^(3/2))-2)*cos(y/sqrt(2)-x/sqrt(2)))/sqrt(2))
 /2)
 +x*sin(y/sqrt(2)-x/sqrt(2))+sin((x-y)/sqrt(2))*(x-y)

See https://trac.sagemath.org/ticket/28750 for downstream. Here is a correct solution, confirmed by the zero.

(%i6) b: sqrt(2)*(x - y)*cos(-1/2*sqrt(2)*(x - y)) + 2*sin(-1/2*sqrt(2)*(x - y));

(%o6) sqrt(2)*cos((x-y)/sqrt(2))*(x-y)-2*sin((x-y)/sqrt(2))
(%i8) diff(b,y)-a;

(%o8) 0

[rtoy]

Imported from SourceForge on 2024-07-09 19:34:29
Created by robert_dodier on 2021-06-17 06:26:51
Original: https://sourceforge.net/p/maxima/bugs/3795/#7cc9

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• labels: --> integrate