> Your point is well taken; however, within a given expression the sqrt
> function should have the same meaning. If not, then why bother having
> solve(a*x^2+b*x+c=0, x) return both roots?
Since the general simplifier does, for example, sqrt(9) --> 3 (not +/- 3), this idea is incompatible with some
built in simplifications.
There are plenty of calculations that use non-principle branches of powers and logs--key hole integration and pac-man
integration come to mind. For the most part, Maxima supports such calculations, but some simplifications, such as sqrt(9) --> 3
and log(%e) --> 1 (not 1 + 2*%pi * integer) potentially break calculations that use a non-principle branch.
In Maxima we have log and plog, but their simplifications are a bit backwards, I think:
Log uses principle branch for floats
(%i7) log(3.4+%i);
(%o7) 0.28605144171732*%i+1.265258580520026
plog doesn't
(%i8) plog(3.4+%i);
(%o8) plog(%i+3.4)
The dlmf sometimes gives different names to related but different functions; see, for example, http://dlmf.nist.gov/4.2 . George Foreman named
five of his sons George. Apparently, it works for George.
--Barton