On Feb 11, 8:10 am, "Dr. David Kirkby" <david.kir...@onetel.net>
wrote:
> On 02/11/11 09:34 AM, daly wrote:

>
> >> FWIW, I just noticed that Mathematica treats 2/1 as an integer and not
> >> as a rational.
>

No, 2/1 is not treated as an integer, it is converted to an integer
and its
history is lost.  That is to say, GCD[2/1 ...]  is never really
computed because
2/1 is changed to 2, and it computes GCD[2 ...]

I think it is pointless to try to gather insight to your concern
about
algebraic categories by typing questions into the (current)
top-level commands in Mathematica. [ though anything could be re-
programmed.
e.g. you could write a whole category system and while you are at it,
write a system for doing polynomial arithmetic using arrays, etc etc.]

But to a pretty good approximation, Mathematica just messes around
with
trees.  It was designed by a physicist, presumably
for physicists, and not for people who want to be so picky about
math :)



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