A specification to get out of some of this tangle may be to define
signum as follows:
signum(real X) --> obvious
signum(complex Z) --> signum(Real(Z))
or consider that
Mathematica defines signum(complex Z) {actually, Sign[Z]}
as a unit vector in the direction Z, so Sign[I] = I.
It also specifies certain other conditions like signs of infinity, and
the possibility of numerical indecision.
RJF
Barton Willis wrote:
> Sure, if realonly worked perfectly, your program would work correctly
> for cubic arguments to signum functions. Thinking that realonly is
> perfect is a reasonable assumption (how hard can that be?)---the user
> documentation hedges:
>
> When `realonly' is `true', `algsys' returns only those solutions which
> are free of `%i'.
>
> That is 100% true (I think) and 100% misleading. Reading that for the
> first time (or second or third...), I'd assume that realonly would
> expunge all nonreal solutions. But it doesn't.
>
> Maxima programming is more interesting than pure numerical
> programming; I regularly learn new things and rely on help and advice
> from this list. And I've been doing this for awhile.
>
> Barton
>
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