Re: binomial(x,x) => 1, but binomial(-1,-1) => 0

I think:

Only if (a,b) in Z^2 and b <= a < 0 there is a problem. (otherwise the
definition using the gamma function just works.)

In the other case we should have a flag like BINOMHACK analagous to
SUMHACK and PRODHACK. If false, the simplification should take place only 
if a and b can be deduced to be in the domain above. Otherwise: 
interactive.

(it could be argued that the same goes for

(C1) sum(1,k,0,n);

(D1)                                 n + 1
(C2) sum(1,k,0,-1);

(D2)                                   0
(C3) sum(1,k,0,-2);

Lower bound to SUM: 0
is greater than the upper bound: - 2
 -- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);)

Note that D2 does not give an error. Very strange. I think, giving an 
error upon C3 is very correct, but D1 should work only if we assume n to 
be a nonnegative integer. Of course, this should be done interactively.)

Martin

PS: I had very subtle errors for my *combinatorics* (!) stuff in 
Mathematica, because of such assumptions. So don't think that in "natural" 
circumstances errors won't occur!