Karl-Dieter Crisman wrote:
x> Absolutely, and I'm not suggesting it should all the time. I think
> that the real question was why the answer was -1, when the function
> (considered as a *function*) is clearly not -1. Which rjf responded
> to more than adequately. I knew radcan was trouble for Sage at times,
> but I hadn't seen this one before.
May i add my two cents to the question? As a physicist, i think that the
main usefulness of a computer algebra system is to find simplifications and
do computations that i cannot do by hand or that need a lot of work. Towards
this aim i am very happy if maxima "simplifies" sqrt(x^2-2*x+1) to x-1,
and i keep in a corner of my head that there is a sign ambiguity. And i am
angry when it omits "obvious" simplifications which render the result
completely impossible to exploit, which unfortunately occurs far too often.
This means that i don't expect that maxima emphasizes elementary formulas
such as sqrt(x^2) = abs(x) which do far more harm than good and are
completely false in the complex domain, that is in the place where things
are interesting. As you are justly saying a computer algebra system has
nothing to do with "functions" in the mathematical sense, and all to do
with algebraic manipulations which belong to the realm of algebraic
geometry, and as such manipulate "multivalued functions" and such stuff.
So at the end, i completely agree with the position of professor Fateman in
your Sage forum. Needless to say, this question regularly appears in the
maxima mailing list.
--
Michel Talon