[Maxima] a .. b
macrakis at alum.mit.edu
Wed Jun 18 11:03:50 CDT 2008
On Wed, Jun 18, 2008 at 11:03 AM, Barton Willis <willisb at unk.edu> wrote:
> Thanks to everybody for the input. I'll delete the auto ceiling / floor
> code. What about float and big float endpoints?
Why don't we define the properties we want for a..b first.
I think it's clear that we want:
Forall x in a..b, x>=a and x<=b
If a>b, then x is empty
If a=b, then either a..b is precisely [a] == [b] or it is empty
Forall x,y in a..b, integerp(x-y)
If integerp(a) then a in a..b
If x in a..b and x+1 <= b then x+1 in a..b
If x in a..b and x-1 >= a then x-1 in a..b
After that, we can choose whether a..b means
A) the integers s.t. a<=x<=b
B) all x s.t. x=a+i and a<=x<=b (where i is an integer)
A(a,b) = B(ceiling(a),floor(b))
B(a,b) = a-floor(a)+A(floor(a),floor(a)+floor(b-a))
Since defining A in terms of B is easier than the other way around, B
looks better -- and it seems to be what commercial Macsyma does.
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