-----Original Message-----
From: Richard Fateman
Sent: Thursday, August 01, 2013 5:13 PM
To: David.Ronis at McGill.CA ; Mailing Maxima
Subject: Re: [Maxima] Atan2 doesn't symplify as expected.
It may not be something that Maxima (or some of
its programmers) apparently agrees with, but
noting that q is greater than zero does not, mathematically speaking,
tell you that sqrt(q) is greater than zero. The
object q still has 2 square roots in general.
Also, if nothing at all is known about q,
sqrt(q^2), which Maxima simplifies to abs(q),
is nonsense as well, since there are two values,
q and -q, neither of which is abs(q).
RJF
I don't think it is necessary to say one interpretation of sqrt(x^2) is
preferable than another, absolutely. The sqrt() function is going to be
part of an argument to a Maxima function that it is passed to by the user.
Clearly if you are working within the scope of pw.mac's (a package with real
numbers as it's main focus) integration command you have to say sqrt(x^2) =
abs(x) because integration requires a function as its argument and functions
by definition are single valued expressions. Given that, the user knows
sqrt(x^2) is going to be, most likely abs(x). If the user want to change
that default interpretation they can always change their input
to -sqrt(x^2). I don't think any user would expect an expression containing
sqrt(x^2) to be interpreted as -abs(x).
Rich