[Maxima-bugs] [ maxima-Bugs-2631766 ] abs((1+%i)^%i) is wrong

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Bugs item #2631766, was opened at 2009-02-23 16:24
Message generated for change (Comment added) made by willisbl
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Dieter Kaiser (crategus)
Assigned to: Nobody/Anonymous (nobody)
Summary: abs((1+%i)^%i) is wrong

Initial Comment:
That is the complex number when we evaluate the expression numerically:

(%i91) rectform((%i+1)^%i),numer;
(%o91) .1548717524642468*%i+.4288290062943678

That is the correct absolute value of the complex number:

(%i92) abs(%);
(%o92) .4559381277659962

Now the wrong result:

(%i93) abs((%i+1)^%i);
(%o93) 1

That is the result when we use cabs:

(%i94) cabs((%i+1)^%i);
(%o94) sqrt(%e^-(%pi/2)*sin(log(2)/2)^2+%e^-(%pi/2)*cos(log(2)/2)^2)

cabs evaluates to the correct numerical result:

(%i95) cabs((%i+1)^%i),numer;
(%o95) .4559381277659962

Remark: It does not help that cabs gets a correct result. The abs function should give a correct result or no result.

I have not studied the bug systematically. I think we have wrong results whenever we have a complex exponent.

Dieter Kaiser

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>Comment By: Barton Willis (willisbl)
Date: 2009-02-23 21:48

Message:
A fix might be to change cabs to $cabs in simpabs:

(defmfun simpabs (x y z)
  (oneargcheck x)
  (setq y (simpcheck (cadr x) z))
  (cond ((numberp y) (abs y))
	((or (arrayp y) ($member y $arrays)) `((mabs simp) ,y))
	((or (ratnump y) ($bfloatp y)) (list (car y) (abs (cadr y)) (caddr y)))
	((taylorize 'mabs (second x)))
	((member y '($inf $infinity $minf) :test #'eq) '$inf)
	((member y '($ind $und) :test #'eq) y)
	((eq (setq z (csign y)) t) ($cabs y))  <---- was (cabs y)
	((member z '($pos $pz) :test #'eq) y)

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

Comment By: Barton Willis (willisbl)
Date: 2009-02-23 21:47

Message:
A fix might be to change cabs to $cabs in simpabs:

(defmfun simpabs (x y z)
  (oneargcheck x)
  (setq y (simpcheck (cadr x) z))
  (cond ((numberp y) (abs y))
	((or (arrayp y) ($member y $arrays)) `((mabs simp) ,y))
	((or (ratnump y) ($bfloatp y)) (list (car y) (abs (cadr y)) (caddr y)))
	((taylorize 'mabs (second x)))
	((member y '($inf $infinity $minf) :test #'eq) '$inf)
	((member y '($ind $und) :test #'eq) y)
	((eq (setq z (csign y)) t) ($cabs y))  <---- was (cabs y)
	((member z '($pos $pz) :test #'eq) y)

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

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