Grouping by units over add - progress, and a couple questions

[C Y , Thu, 19 May 2005 18:40:13 -0700 (PDT)]:
> In general, it is meaningless to pose an expressin a^b where b is a
> quantity with units.

Not sure: In any book on liquid state physics you are likely to find
expressions like rho*log(rho), rho being of dimension 1/volume.  Which
is, of course, equivalent to log(rho^rho).  It may seem meaningless,
but that is only because some not very interesting quantities like,
e.g., -rho*log(...) with ... of appropriate dimensions are often left
out.

OTOH, it may well be that people who want to do their calculations in
this way simply should not use the units package.

> In general, it is meaningless to evaluate a trigonometic function with
> a unit bearing argument, e.g. sin(a*b), where b is a unit other than
> rad or deg or some other numerical factor.

But rad and deg are not really units but simple numbers. rad = 1, deg
= pi/180.

Also, suppose b = 1/meter.  Why should sin(a*b) be prohibited?  Do you
require the dimensions of a (which would be a length) to be manifest
in all calculations?

Regards,

Albert.