Hi, I usually just watch the list for features and so on, but I have
two questions about this sqrt thing.
1) Maybe I am doing this naively, but I don't get the following
apparent inconsistency:
Maxima 5.20.1 http://maxima.sourceforge.net
using Lisp ECL 10.2.1
<snip>
(%i1) float(%i);
(%o1) %i
(%i2) float(sqrt(%i));
1/4
(%o2) 1.0 (- 1)
and something similar with bfloat. Just curious about this behavior;
I might have otherwise expected 1.0(-1)^(1/2) from the first thing.
Is the symbol %i considered to be both a float and a symbolic
constant?
2) Why do most CAS seem to talk about principal roots for roots of
negative numbers, but not for positive numbers? I've seen this on the
Sage list and it seems like proprietary programs also assume sqrt(1)=1
and not -1 (or the set of both) unless you ask for all of them. But
in some sense -1 should be thought of as a generator for the group of
square roots of unity, not +1. Is it maybe just arbitrary then which
square root of other numbers one chooses? I don't ask this to start
an argument, I am just curious as to the historical reasons for this
(which I would, naively, guess are practical, since most users of
sqrt(1) probably want the positive root).
Thanks! I don't mean to derail the technical discussion, these
questions just seemed apropos and I've been thinking about them for a
while.