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

Chris Fleming wrote:


<snip>

 The only problem I can 
> see is to make Maxima understand that something like int1 + int2 could 
> be simplified to int3


This is a serious problem, addressed in part by a masters project
done under my direction by Neil Soiffer circa 1980.  Essentially,
find the minimum number of "arbitrary constants" in a rational
expression of several variables that maintains the same amount of 
arbitrariness.  The
restriction to rational functions makes it solvable by resultants,
but the more general problem has not been addressed, as far as I know.


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



This would not guarantee realness; e.g.  solve (sin(i*x)=y, x).


> 
> 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


This also is something I've worried about, but the general problem
is to keep the pieces going through some more calculations without
getting an enormous blow-up in complexity.  Simplifying geometric
constraints is needed to cut back on this, and it is tough.
I believe a masters' project by Sam Dooley looked at making
a simplifier work with this approach.  Didn't get too far
though.