Daniel Lemire wrote:
>
> Good day,
>
> I'm not sure what you are talking about, both exp() and log() are
> one-to-one (bijective) functions.
This is false in general, since exp(x)=exp(x+4*pi*i), and x is not
equal to x+4*pi*i.
Why do you think that the solution of logarithmic and exponential
equations is of any interest over the real numbers?
>
> So,
>
> A = B
>
> if and only if (assuming A,B>0)
>
> log(A) = log(B)
>
> and
>
> A = B
>
> if and only if
>
> exp(A) = exp(B).
>
> Of course, assuming real numbers (that's what I do here). So, I wasn't
> expecting anything *unsafe* from Maxima.
>
> Even so, I would expect even the most stupid computer algebra system to
> simplify
>
> A* sin^2 (x) + A * cos^2(x)
>
> to
>
> A
>
> otherwise, it might as well not exist.
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?
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.
It is not unusual in the CAS business to surprise people in
that some things that are easy for humans turn out to be,
in general, not computable. And other things that humans
find difficult, or may think are impossible (like finding all
factors of a polynomial of high degree), are easily computed.
>
> I did put "Newbie" in the subject line to indicate that I didn't
> necessarily know the software very well. So I'm not saying Maxima is
> useless, I'm just saying that it appears to be useless right now to me.
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.
>
> > You say,
> > Again, it would seem like Maxima fails miserably... and I'm not even
> > taking a very difficult case!
> >
> > Why not try some function f(x)= stuff,
> > where f is sin, cos, linear, quadratic, cubic, quartic.
> >
> > instead of f(x)=g(x) where neither f nor g
> > has a single-valued inverse.
>
> --
> Daniel Lemire, Ph.D.
>
> http://www.ondelette.com/
>
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