Viktor T. Toth wrote:
first and foremost, I think we should make sure that no code should
> produce a mathematically incorrect result, even if it fails to produce the
> "desired" result (i.e., it's better to not simplify an expression than to
> simplify it incorrectly.) I believe this attitude is essential if Maxima is
> intended to be used as a serious research tool.
I think you underestimate the difficulty of this.
Just to pick one example, consider
sum(a[i]*x^i,i,0,inf);
subst(0,x,%) gives 0.
sum(a[i]*x^i,i,0,5);
subst(0,x,%) give a[0]
I think that the first of these is incorrect, but fixing it is
hard, without breaking something else.
The commercial Macsyma does the same thing even though
I suspect this bug was pointed out many years ago.
Mathematica used to have the same bug, but now it seems that it
cures this by leaving 0^i unsimplified. Even if the sum
is from 1 to inf.
RJF