[Maxima-bugs] [ maxima-Bugs-626721 ] logarc of atan2 wrong

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Bugs item #626721, was opened at 2002-10-22 03:15
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: logarc of atan2 wrong

Initial Comment:
res : logarc(atan2(y,x))$
rectform(res),y=1,x=-1;
     => -%pi/4

BUT

atan2(1,-1) => 3*%pi/4

The fix is to change the formula in $logarc and in 
simpatan2.  Currently, logarc(atan2(y,x)) => logarc(atan
(y/x)), which gives incorrect results as above.

This formula should be replaced by

  -%i*log((y+%i*x)/sqrt(x^2+y^2))





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>Comment By: Raymond Toy (rtoy)
Date: 2006-11-08 23:26

Message:
Logged In: YES 
user_id=28849

Oops.  I think the formula was intended to be
-%i*log((x+%i*y)/sqrt(x^2+y^2)).

That produces the correct values.  At least
factor(rectform(<formula>)) produces atan2(y/r,x/r) with r =
sqrt(x^2+y^2).

It would be nice if atan2 simplified out the denominator to
leave only atan2(y,x).

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Comment By: Raymond Toy (rtoy)
Date: 2006-11-08 23:13

Message:
Logged In: YES 
user_id=28849

Isn't this formula also wrong?  For y=1, x=-1, the formula
becomes -%i*log((1-%i)/sqrt(2)).  But log is the principal
log so we still get -%pi/4.

I think it would be better to make atan2 be in the range
(-%pi,%pi].

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