Good day,
> This is false in general, since exp(x)=exp(x+4*pi*i), and x is not
> equal to x+4*pi*i.
I specifically said that I was assuming all my variables and constants
to be real. I said it several times, even repeating it quite clearly in
the message you are answering to.
> Why do you think that the solution of logarithmic and exponential
> equations is of any interest over the real numbers?
I won't even answer that question. It *obvious* why logs and exps are
interesting over real numbers!
> Aha, so you must in your own mind have an algorithm in mind that
> will reduce all expressions involving sin^2 and cos^2 to simplest
> form. In which case what would you like for
> sin^2x + 2*cos^2x? cos^2x+1 or 2-sin^2x ? And by what
> algorithm did you achieve this?
I'm not an algebra specialist. I don't have such an algorithm, however
both Maple and Mathematica behave as I expect in such simple cases (and
in much more difficult cases also).
> Your expectation may further be reduced by the knowledge that
> Daniel Richardson proved that one cannot write an algorithm
> to determine if an expression is zero or not, given that it
> involves rational combinations of one variable, the integers,
> the sin and abs functions, and pi.
I have no trouble believing that result. Nobody ever said that a
computer algebra system had to be perfect.
> It may very well be useless to you. I am surprised however
> that Maple and Mathematica meet your needs, since they have
> each been eliminated as unsuitable for the calculus class
> at UC Berkeley: they gave wrong answers.
Do you have a reference to this comparative study? I'd like to have a look! It is exactly the type of thing I'm looking for right now!
--
Daniel Lemire, Ph.D.
http://www.ondelette.com/