On Wed, Jul 9, 2008 at 8:43 PM, Gabriel Dos Reis
<[EMAIL PROTECTED]> wrote:
> ...
> In the field of fraction of polynomial, the fact that 1/(2d) is well
> defined seals no doubt. It does not matter whether d can take
> on the value zero. That is just a simple fact. That is one of
> reasons why simplification of expressions that assume
> fraction of polynomials prove inadequate some times.
>
If "d can take on the value zero" doesn't that imply we are thinking
of '1/(2d)' as a function?
Isn't the following result another example such an error?
(1) -> q:=((x^2-1)/(x-1))
(1) x + 1
Type: Fraction Polynomial Integer
(2) -> q(1)
(2) 2
Type: PositiveInteger
Surely the fact that we can write (2) means this simplification is unjustified.
> Have a look at this wonderful paper by James Davenport.
>
> "Equality in Computer Algebra and Beyond"
>
Thanks, I will review it again. You have referred to this paper before:
http://sourceforge.net/mailarchive/message.php?msg_name=87od8i6aej.fsf_-_%40gauss.cs.tamu.edu
In the abstract from which you quote Davenport writes:
"For example, we refer to Q(x) as "rational functions", even though
(x^2-1)/(x-1) and x+1 are not equal as functions from R to R, since
the former is not defined at x=1, even though they are equal as
elements of Q(x)."
But as I recall he does not deal with this issue in greater
specificity in the rest of the paper.
For the accessibility challenged here is an alternate (free) link:
http://www.calculemus.net/meetings/siena01/Papers/Davenport.ps
to this paper.
Regards,
Bill Page.
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