[Maxima-bugs] [ maxima-Bugs-3027529 ] integrate(logarc(atan2(y, x), y) -> Divison by zero

[SourceForge.net <no...@so...>]

Bugs item #3027529, was opened at 2010-07-09 20:57
Message generated for change (Tracker Item Submitted) made by crategus
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3027529&group_id=4933

Please note that this message will contain a full copy of the comment thread,
including the initial issue submission, for this request,
not just the latest update.
Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Dieter Kaiser (crategus)
Assigned to: Nobody/Anonymous (nobody)
Summary: integrate(logarc(atan2(y,x),y) -> Divison by zero

Initial Comment:
When we try to integrate the equivalent logarithmic expression for atan2 we get an error:

(%i34) integrate(logarc(atan2(y,x)),x);
Division by 0
 -- an error. To debug this try: debugmode(true);

(%i35) integrate(logarc(atan2(y,x)),y);
Division by 0
 -- an error. To debug this try: debugmode(true);

The error occurs in ratint. ratint tries to integrate the following expression:

(%i36) expr;
(%o36) -x^3/(%i*y^3+x*y^2+%i*x^2*y+x^3)

(%i37) integrate(expr,x);
  0: (RATINT
      ((MTIMES SIMP) ((MEXPT SIMP) $X 3)
       ((MEXPT SIMP)
        ((MPLUS SIMP) ((MEXPT SIMP) $X 3)
         ((MTIMES SIMP) $%I ((MEXPT SIMP) $X 2) $Y)
         ((MTIMES SIMP) $X ((MEXPT SIMP) $Y 2))
         ((MTIMES SIMP) $%I ((MEXPT SIMP) $Y 3)))
        -1))
      $X)
Division by 0
 -- an error. To debug this try: debugmode(true);

Dieter Kaiser

----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3027529&group_id=4933