On 9/9/2010 4:49 PM, Richard Hennessy wrote:
....
>
> Why do you insist that inf can be added, subtracted, multiplied and
> exponentialized (or squared). It is not a number, don't apply the
> "numbers only" simplifiers to it.
In fact, it is not the "numbers only" simplifier that is at issue. It
is the "symbols" simplifier that must be modified to check, at some
cost, for such special items.
For any symbol x the simplifier does transformations like x+x ->
2*x. x/x -> 1. x-x=0. etc.
>
> inf - inf = inf - inf
> inf + inf = inf + inf,
> inf - inf = inf - inf
> minf + minf = minf + minf
> minf - minf = minf - minf
> inf - minf = inf - minf
> minf - inf = minf - inf
> infinity + inf = infinity + inf
>
> Just leave it as is.
Here's (one of) the problems. You can no longer simplify x-x ->0.
The symbol x might be one of those nasty items.
Worse, x might be an indeterminate or "variable", and later could be
assigned a value like infinity. So instead of having
a value 0, you have to say "0 unless x is a nasty item"
You don't actually need infinity to get in trouble, since x/x->1 is
really "1 unless x is zero".
The choice "just leave it as is" is untenable unless you have an
extremely weak system model.
For example, represent and operate on polynomials with integer
coefficients. No division allowed.
Certainly too weak to be a serious alternative to Maxima.
RJF