This is interesting but last time I checked signum and unit_step return a noun form for complex arguments. Abs() does support
complex arguments and I don't like expressing piecewise functions in terms of the abs() function because of that and other reasons.
The equivilence x*signum(x) = abs(x) is only true for the reals. If z is complex then z*signum(z) = abs(z) fails completely to mean
the same thing.
Rich
----- Original Message -----
From: "Richard Fateman" <fateman at cs.berkeley.edu>
To: "Barton Willis" <willisb at unk.edu>
Cc: <rvh2007 at comcast.net>; <fateman at EECS.Berkeley.EDU>; <maxima at math.utexas.edu>
Sent: Saturday, December 20, 2008 12:52 PM
Subject: Re: [Maxima] pw.mac version 2.3.1
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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