# [Maxima] sign((-1)^number): Inconsistent handling of numbers

Richard Fateman fateman at cs.berkeley.edu
Sat Nov 29 16:05:07 CST 2008

```I think that you ultimately can reduce these questions to a single
question, which
is whether (or when) the logarithm function is multivalued or not.

a^b   is  exp(b*log(a))

if you want to return, for non-positive a,  several values, then exp()
has several values. etc.
As for getting different performance from bfloat, float, etc, I think
they should do the same thing to
the extent possible.

RJF

Dieter Kaiser wrote:
> An oberservation concerning the \$sign function of Maxima:
>
> We call with an imaginary argument and get an expected error message:
>
> (%i3) sign((-1)^(1/2));
> `sign' called on an imaginary argument:
> %i
>  -- an error.  To debug this try debugmode(true);
>
> Now we do the same with a float representation. We get a result:
>
> (%i5) sign((-1)^(0.5));
> (%o5) neg
>
> When we use a bigfloat we get again the error:
>
> (%i7) sign((-1)^(0.5b0));
> `sign' called on an imaginary argument:
> %i
>  -- an error.  To debug this try debugmode(true);
>
> We get the same results when we use any other half integral rational number.
>
>
> Now we test rational numbers with an odd denominator. The following two results
> are exptected:
>
> (%i11) sign((-1)^(1/3));      /* simplifies to -1 */
> (%o11) neg
> (%i12) sign((-1)^(2/3));      /* simplifies to +1 */
> (%o12) pos
>
> When we do the same with float values we always get NEG as an answer:
>
> (%i13) sign((-1)^float(1/3));
> (%o13) neg                     /* OK */
> (%i14) sign((-1)^float(2/3));
> (%o14) neg                     /* Should be pos */
>
> If we use bigfloat numbers we get errors.
>
> (%i15) sign((-1)^bfloat(1/3));
> `sign' called on an imaginary argument:
> %i
>  -- an error.  To debug this try debugmode(true);
>
> (%i16) sign((-1)^bfloat(2/3));
> `sign' called on an imaginary argument:
> %i
>  -- an error.  To debug this try debugmode(true);
>
> The reason is that for bigfloat numbers the expression is evaluated to a complex
> root (see SF[619927]).
>
> (%i17) (-1)^bfloat(1/3);
> (%o17) 8.660254037844386b-1*%i+5.0b-1
>
> We get different results for rational, float and bigfloat numbers.
>
> I think one problem is that the routine sign-mexpt in compar.lisp does not
> handle the case of a negative base completely. For all cases not known by the
> algorithm the default return value is the sign of the base and that is in the
> cases above a negative sign.
>
> Do you think the inconsistent handling of numbers is a bug?
>
> Dieter Kaiser
>
>
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>

```