#2554 sign(sqrt(-x^2-x^4)) => zero

[Stavros Macrakis]

As the title says, sign(sqrt(-x^2-x^4)) => zero. This should give an "argument cannot be imaginary" error as does sign(sqrt(-1-x^2)).

A consequence of this bug is abs(sqrt(-x^2-x^4)) => 0.

[Barton Willis]

Same bug, I suppose

$ ./maxima-local
Maxima 5.28.0_232_g5b9ec8e http://maxima.sourceforge.net
using Lisp Clozure Common Lisp Version 1.8-r15286M (WindowsX8664)

(%i1) assume(p <=0)$

(%i2) csign(sqrt(p));
(%o2) zero

[Barton Willis]

The bug is almost surely in the function sign-mexpt--here is a portion of this
code. On the first line sign-base is $nz, so sign-base is set to $zero. After that
the global sign is set to sign-base. The final conditional doesn't have a clause for
$zero, so sign remains zero. A quick cure would be append a clause ((eq sign-base '$zero) ..., I suppose.

        ((eq sign-base '$nz)
         (setq sign-base '$zero)
         (tdzero base1))
        (t (setq sign-base '$pz)
           (tdpz base1)))))
   (cond ((eq sign-expt '$neg)
      (cond ((eq sign-base '$zero) (dbzs-err x))
        ((eq sign-base '$pz)
         (setq sign-base '$pos)
         (tdpos base1))
        ((eq sign-base '$nz)
         (setq sign-base '$neg)
         (tdneg base1))
        ((eq sign-base '$pnz)
         (setq sign-base '$pn)
         (tdpn base1)))))
   (setq sign sign-base))
  ((eq sign-base '$pos)
   (setq sign '$pos))
  ((eq sign-base '$neg)
   (if (eq evod '$odd)
       (setq sign '$neg)
     (setq sign (if *complexsign* '$complex '$pn)))))))

[David Scherfgen]

I don't think it should raise the "argument cannot be imaginary" error, because -x^2-x^4 is not strictly negative. For x = 0, it's zero. This is a major limitation of sign. It has no way to say "zero or complex". Basically all possible answers it can return are wrong or misleading.
I think the answer zero of sign should be interpreted as "zero, if not complex".
So maybe this is an issue of how sign's return value should be interpreted.