Adding new object types WAS: Operations on inf

If you want to see how I think one should design code for arithmetic-like
objects generically (by the author of the bfloat code --me)
then look at the generic lisp code I posted in
http://www.cs.berkeley.edu/~fateman/generic

Adding it to bfloat doesn't seem like a good approach, but there are
probably worse approaches.
If we wanted to do this right, we could start with Axiom.
RJF


> -----Original Message-----
> From: maxima-bounces at math.utexas.edu 
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Robert Dodier
> Sent: Thursday, March 08, 2007 10:16 PM
> To: Stavros Macrakis
> Cc: Maxima List
> Subject: Re: [Maxima] Adding new object types WAS: Operations on inf
> 
> Stavros, unfortunately I am rather uneasy with this proposal 
> on the whole.
> 
> > For objects with number-like behavior, I believe the easiest way
> > we can do this is to piggyback on the existing bfloat code.
> 
> Well, what is it about the bigfloat simplification dispatch that makes
> it fast enough to be practical? That is the aspect of bigfloats that
> I think we need to copy for other number-like objects.
> 
> > Let's use ((bigfloat simp interval) ...), ((bigfloat simp 
> quadfloat) ...)
> > etc. to represent new data types.
> 
> I dunno. This makes me very uneasy. I don't like objects which
> aren't really bigfloats masquerading as such. At present we have
> (MLIST CF) for continued fractions, which was a very weak choice,
> frankly. I don't want new objects like that.
> 
> > This seems to me by far the simplest way of handling extensions
> > like the ones you're talking about.  What is unavoidable, though,
> > is going through the code to remove incorrect assumptions, such
> > as trichotomy (compare the interval [2,5] with [3,4] or [1,3]) and
> > realness (currently, all things that Maxima considers to be 
> "numbers"
> > are real).
> 
> I don't think it's much of win to reuse some of the identities now
> applied to bigfloats for other number-like objects. It's much more
> important to be able to distinguish the identities applied to each
> type of object. One of Maxima's biggest problems at present
> (IMNSHO) is that it is more or less impossible to know what are the
> identities which Maxima applies to a given kind of expression.
> I don't want to make the problem any worse than it is.
> 
> > This technique could be applied to Gaussian integers, bfloat
> > complexes, float intervals, even distributions (with various rules
> > of combination) etc. etc.
> 
> I agree that Maxima should be able to handle all of these,
> but not by the method mentioned above.
> 
> FWIW
> Robert
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