===copy my post on sandbox here:=====
Yes, polynomial (x-1) might be evaluated to 0 (all of
Integer,Float,Complex?),
but this doesn't change the matter of (x-1) is not a zero-polynomial.
Well, do you think (x**2-1)/(x-1) = (x+1) is legal and guaranteed in the
domain of
polynomial? But it's not in the domain of Float/Integer.
You don't want to modify the rule of polynomial to accommodate this, right?
On Wed, Jul 9, 2008 at 10:38 AM, Bill Page <[EMAIL PROTECTED]>
wrote:
> On Wed, Jul 9, 2008 at 7:29 AM, Gabriel Dos Reis wrote:
> > On Wed, Jul 9, 2008 at 12:35 AM, Bill Page wrote:
> >
> >> *yixin.cao wrote:* -- In the light of polynomial, (2d) is a
> >> non-zero polynomial, so that it's always safe to write (1/(2d))
> >>
> >> If a value of 0 is subsituted for d in this "non-zero polynomial"
> >> then in what sense is '1/(2d)' safe?
> >
> > This is the classical difference between a function (defined by a
> > polynomial) and a polynomial.
> >
> > There is no doubt that -- if d is the unknown -- then 2d is a non-zero
> > polynomial and as such has an inverse in the field Q(d).
> >
>
> But is computing in the field Q(d) "safe" if we eventually intend to
> replace d with some non-symbolic value? Isn't there a possibility that
> such computations could lead to incorrect results due to (for example)
> implicit divisions by 0? It seems to me that an inverse in Q(d) might
> have no counterpart in Q.
>
> Regards,
> Bill Page.
>
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