[Maxima-bugs] [ maxima-Bugs-1860487 ] MONSTERTRIG endless recursion

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Bugs item #1860487, was opened at 2007-12-29 10:43
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Category: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Robert Dodier (robert_dodier)
Assigned to: Nobody/Anonymous (nobody)
Summary: MONSTERTRIG endless recursion

Initial Comment:
MONSTERTRIG tries to reduce some trig expressions and start over. However I've encountered an expression for which the attempted reduction has no effect, so it loops endlessly.

e.g.

trace (integrate, ?monstertrig);
integrate (x*(cos(2*x) + sin(x)), x);
 =>
1 Enter integrate [x*(cos(2*x)+sin(x)),x]
 1 Enter ?monstertrig [x*(cos(2*x)+sin(x)),x,x]
 1 Exit  ?monstertrig false
 1 Enter ?monstertrig [x*(cos(2*x)+sin(x)),x,2*x]
 2 Enter integrate [?new\-var\-15974*(cos(?new\-var\-15974)
                 +sin(?new\-var\-15974/2))
 /2,?new\-var\-15974]
  2 Enter ?monstertrig [?new\-var\-15974*(cos(?new\-var\-15974)
                 +sin(?new\-var\-15974/2)),?new\-var\-15974,
 ?new\-var\-15974/2]
   3 Enter integrate [2*?new\-var\-15975
 *(cos(2*?new\-var\-15975)+sin(?new\-var\-15975)),
 ?new\-var\-15975]
    3 Enter ?monstertrig [?new\-var\-15975*(cos(2*?new\-var\-15975)
                 +sin(?new\-var\-15975)),?new\-var\-15975,
 ?new\-var\-15975]
    3 Exit  ?monstertrig false

... etc etc.

Here's the relevant code from MONSTERTRIG (src/sin.lisp).

        ;; We have trig(c*x+b).  Use the substitution y=c*x+b to
        ;; try to compute the integral.  Why?  Because x*sin(n*x)
        ;; takes longer and longer as n gets larger and larger.
        ;; This is caused by the Risch integrator.  This is a
        ;; work-around for this issue.
        (let ((c (cdras 'c arg))
          (b (cdras 'b arg))
          (new-var (gensym "NEW-VAR-")))
          (let ((new-int (div ($integrate (maxima-substitute (div
(sub new-var b) c)
                                 var exp)
                          new-var)
                  c)))
        (return-from monstertrig (maxima-substitute *trigarg* new-var
new-int)))))

risch has no trouble with the example shown above, although the comments in MONSTERTRIG suggest risch has trouble in some cases.


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