> There are 2 square roots. Sqrt(x^2) has 2 values, x and -x.
Generally Maxima assumes that sqrt means the principal square root, not a multivalued square root; for example
(%i1) sqrt(9);
(%o1) 3
(%i2) sign(sqrt(x));
(%o2) pz
For the log function, Maxima has plog (principal log) and log (multivalued log); sometimes these functions behave as they
should, sometimes not:
Correct: nounform for log(1+%i), rectangular form for plog
(%i6) [plog(1+%i), log(1+%i)];
(%o6) [log(2)/2+(%i*%pi)/4,log(%i+1)]
Wrong: assumes principal log
(%i10) log(%e);
(%o10) 1
Additionally, both rectform and imagpart assume that log and sqrt are not multivalued functions. Similar to log and plog, I would
think that it would be useful to have principal and multivalued versions of sqrt and general powers. Of course, if at all possible, different
functions should have different identifiers. The US Federal government, however, decided that it's OK to have z^a mean two different things
(see http://dlmf.nist.gov/4.2#iv).
--Barton