Donna L.Y. wrote:
> Here are some examples of the class of problems that I am referring  
> to when I concurred that it might be interesting to know the  
> difference between 1r3 and 111r333: ...

Why do you phrase this issue that way?

Why not phrase it as, for example, the difference between the ratio
represented by 1 3 and the ratio represented by 111 333.  Or, as
the difference between the expression '1%3' and the expression
'111%333'.  Or append the letter 'x' to those expressions.  Or,
...

?

After all, internally, the number 1r3 is represented as something
analogous to (<(,1);,3), and the number 111111r333337 is represented
as something analogous to (<111 111;333 337).  If J can do that
internally, is there some reason why application code can't resort
to similar measures?

P.S. in your earlier message, where you wrote:

Max μ = α,χ

you did not define μ.  Perhaps you mean that μ is an n element
vector where the ith element of μ is either the ith element of
α or the ith element of χ, whichever is larger.  But the notation
I'm familiar with would have expressed that as μ = Max α,χ, and
that still would not indicate the relevance of μ to the problem.
(And, yes, I could probably look this up, but I'm not very
energetic at the moment.)

Anyways... clarification needed...

-- 
Raul

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