[Maxima-bugs] [ maxima-Bugs-2848682 ] abs(log(-1)) --> -log(-1)

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Bugs item #2848682, was opened at 2009-09-01 21:51
Message generated for change (Tracker Item Submitted) made by crategus
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Category: Lisp Core - Assume
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Dieter Kaiser (crategus)
Assigned to: Nobody/Anonymous (nobody)
Summary: abs(log(-1)) --> -log(-1)

Initial Comment:
Maxima always simplifies abs(log(x)) to -log(x) if x<1:

(%i38) assume(x<0)$
(%i39) abs(log(x));
(%o39) -log(x)

This happens for negative numbers too:

(%i40) abs(log(-1));
(%o40) -log(-1)

As a consequence the absolute value of e.g. log(-1) is imaginary:

(%i45) rectform(abs(log(-1)));
(%o45) -%i*%pi

This is the correct result:

(%i46) abs(rectform(log(-1)));
(%o46) %pi

The reason is that for every argument x<1 the function sign returns neg. 

(%i42) sign(log(x));
(%o42) neg

But this is true only for 0 < x < 1. For x<0 sign should return pnz.

This could be a correction to the routine sign in compar.lisp:

((eq (caar x) '%log)
 ;; Return a negative or positive sign only when the argument
 ;; is a real positive value in all other cases '$pnz.
 (cond ((eq (setq sign (compare (cadr x) 0)) '$neg)
        ;; Negative argument.
        (setq sign '$pnz))
       (t 
        ;; Positive argument to the Log function.
        ;; Check argument < 1 or > 1.
        (compare (cadr x) 1))))

Dieter Kaiser

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