I agree--rather than just having a signed/unsigned infinity ring, I
think there should be an extended ring for Z, Q, R, C--both signed
and unsigned when there is an absolute order. When does the concept
of infinity make sense for a given ring? 1 (or 2)-point
compactification? (not for Q), ordering (not for C), maybe an
unbounded valuation (making "p-adic infinity" equal to zero?)
Implementation-wise, this could be accomplished via a generic wrapper
around the rings and their elements (which I think could still be
quite fast, and coercion would be natural and efficient too, not to
mention the difficulties and inefficiencies raised by having multiple
types for a single parent, or Integers with non-integer-ring parents).
The default sage oo would be +Infinity in Z \union {\pm \infty}.
On Jan 24, 2008, at 1:15 PM, David Roe wrote:
> So perhaps the solution to your problem is the extended integers
> (or extended rationals). This needs some work (both in terms of
> speed and with having multiple types for elements of the same
> parent), but it does have the benefit of returning 1 as the answer
> to 1 + 0/infinity. Perhaps the default sage infinity should be the
> infinity of the extended integers, and there's a coercion map from
> the extended integers to the extended rationals to the signed
> infinity ring to the unsigned infinity ring, as well as coercions
> from the integers to the extended integers and the rationals to the
> extended rationals.
> David
>
> On Jan 24, 2008 12:48 PM, Burcin Erocal <[EMAIL PROTECTED]> wrote:
>
> Hello,
>
> Today I witnessed a mathematica user struggling with Sage because of
> the way Sage handles infinity. On trac #1915 you can see an example.
>
> On Thu, 17 Jan 2008 09:52:32 -0500
> David Harvey <[EMAIL PROTECTED]> wrote:
>
> > Question: why does the "unsigned infinity ring" not have a zero
> > element, whereas the "(signed) infinity ring" has a zero?
> >
> > This is okay:
> >
> > sage: 0 / Infinity
> > Zero
>
> I don't think this is okay. In this case we get
>
> sage: 1 + 0/Infinity
> A positive finite number
>
> If 0/Infinity is 0, the result of this should be 1.
>
> > But this is way confusing:
> >
> > sage: oo = UnsignedInfinityRing(Infinity)
> > sage: 0 / oo
> > A number less than infinity
> >
> > I totally expected the last output to be Zero. But it can't be,
> > because the UnsignedInfinityRing doesn't have a zero element.
>
> I would also expect the output to be zero. Moreover, there should be a
> way of returning a numeric zero from these operations. Otherwise the
> coercion model gets confused, and everything ends up being coerced
> into
> "The Infinity Ring".
>
> sage: Infinity.parent()
> The Infinity Ring
>
>
> Thoughts?
>
> Burcin
>
>
> >
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
