[Maxima-bugs] [maxima:bugs] #3795 incorrect integration

[Robert D. <rob...@us...>]

Appears that this bug was fixed somewhere between Maxima 5.47 and 5.48. I will try to pin down the specific commit.


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**[bugs:#3795] incorrect integration**

**Status:** open
**Group:** None
**Labels:** integrate 
**Created:** Mon Jun 07, 2021 02:24 PM UTC by kcrisman
**Last Updated:** Thu Jun 17, 2021 06:26 AM UTC
**Owner:** nobody


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
~~~


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