Re: What should "solving" really mean, some literature.



On Saturday 06 October 2001 15:49, you wrote:
> I have a suggestion that may require alot of programming, but it is a
> feature that I have always wanted in a CAS but never seen.
>
> When solving an equation such as
>
> exp(1) = exp(x) for x
>
> return an infinite set of solutions
>
> x = {1 + 2*k*pi*i} | k is an integer
> . . . 

Hi, Chris,
I have seen something like that, I think it was Reduce. (There is a demo 
version).

But to me it wasn't that impressive, it's more like a data base with some 
extra information, I bet if you ask for %I^%I the answer will be (like in 
maxima and in Mathematica) exp(-Pi/2) (try polarform(%I^%I)).

And if you where a CAS, what would you do with exp(x)=sin(x)? I can't see 
another way of finding the real solutions by some Newton + the insight that 
those solutions are fairly close to -n*Pi. And if it comes to complex 
solutions (up to now I found one,  around 0.36270205612105 + i* 
1.133745919413753); I confess I learned a lot about maxima, that's why I'm 
trying to solve it, but I can't see a solver able to do it without help. 

By the way, this complex solution produced a lot of strange behaviour, but 
I'll put that in another mail.

Jurgen