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

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

so everytime this happens, there would be a k1, k2, k3 ... or perhaps 
just saying int1, int2, ... would be better.

And then just do calculations on the set as normal. I am thinking that 
when I work in the complex plane, this is how I would do it, and my 
understanding of CAS is that it seems possible. The only problem I can 
see is to make Maxima understand that something like int1 + int2 could 
be simplified to int3

And people that only want real solutions, then there could be a flag so 
the integer will be assumed to be zero.

I also had one other feature that I have always wanted, and that is when 
you try to do something funny like integrate x^p for x, instead of 
having to give information about p, just return a piece wise function 
for different values of p