[Maxima-bugs] [ maxima-Bugs-1607567 ] trigreduce([atan(sin(a)/cos(a))]) => [ atan(tan(a)) ] (FIX)

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Bugs item #1607567, was opened at 2006-12-02 16:49
Message generated for change (Comment added) made by rtoy
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Category: Lisp Core - Trigonometry
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: trigreduce([atan(sin(a)/cos(a))]) => [ atan(tan(a)) ]  (FIX)

Initial Comment:
trigexpand( [ atan(sin(a)/cos(a)) ] ) => atan(tan(a))
        (UNSIMPLIFIED!)

whereas

  trigexpand( atan(sin(a)/cos(a)) ) => a

and

  atan(tan(a)) => a

Though the simplification atan(tan(a))=> is questionable (it needs to do reduction), it is weird that putting the argument to trigexpand in a list changes the behavior.




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>Comment By: Raymond Toy (rtoy)
Date: 2006-12-08 21:13

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This change works for me.  I get a and [a] for results. I'll apply the fix
soon.

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Comment By: Stavros Macrakis (macrakis)
Date: 2006-12-08 14:31

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The problem is that sp1 isn't handling simplification quite right. The
result is
  ((MLIST SIMP) ((%ATAN) ((%TAN SIMP) $A)))
The %ATAN doesn't have a SIMP flag, though it is within a SIMP
expression.

The fix is simple.  In trgred.lisp, function sp1:

BEFORE:
	((mbagp e) (cons (car e) (mapcar #'sp1 (cdr e))))
AFTER:
	((mbagp e) (cons (car e) (mapcar #'(lambda (q) (simplifya (sp1 q))) (cdr
e))))

Interestingly, trigreduce doesn't go inside unknown functions at all,
e.g.

        trigreduce(  f(sin(x)/cos(x))  )

doesn't do anything at all.  I wonder if there is a good reason for this?


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Comment By: Raymond Toy (rtoy)
Date: 2006-12-08 13:15

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With current CVS, the example with sin(x)^2 gives the same results whether
it's a list or not.

Also, if you :lisp (trace $trigreduce), you can see that
trigreduce([atan(sin(a)/cos(a))]) returns [atan(tan(a))] and
trigreduce(atan(sin(a)/cos(a)) returns atan(tan(a)).  Something after
trigreduce returns causes the simplification to happen.  Perhaps in meval
or something?

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Comment By: Stavros Macrakis (macrakis)
Date: 2006-12-04 12:40

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Other simplifications also don't happen:

   trigreduce( sin(x)^2 ) =>   (1-  cos(2*x))/2            (OK)
   trigreduce([sin(x)^2]) => [ (2-2*cos(2*x))/4 ]       (?)

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Comment By: Stavros Macrakis (macrakis)
Date: 2006-12-04 12:30

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Sorry, it's trigreduce in Maxima 5.10.0 GCL 2.6.8 Windows2k Athlon

  trigreduce(atan(sin(a)/cos(a))) => a
  trigreduce([atan(sin(a)/cos(a))]) => [atan(tan(a))]

PS I should always cut and paste rather than retyping....


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Comment By: Raymond Toy (rtoy)
Date: 2006-12-04 11:49

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What version?  

With 5.10.0 and cmucl, trigexpand([atan(sin(a)/cos(a))]) =>
[atan(sin(a)/cos(a))]

Corresponding result if the arg is not a list.

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Comment By: Stavros Macrakis (macrakis)
Date: 2006-12-02 16:53

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Oops, it's actually

trigexpand( [ atan(sin(a)/cos(a)) ] ) => [ atan(tan(a)) ]
(UNSIMPLIFIED!)

It doesn't simplify atan of tan, but it does preserve the list...


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