Craig Citro wrote:
>> Okay, that seems like a valid point, though I still disagree. I think
>> that we have two levels of consistency here: consistency with the
>> function and consistency with the concept of interval arithmetic. I
>> think that in this case, the interval arithmetic requirement is more
>> specific, so you should be consistent with having intervals.
>>
>
> Well, I guess this depends on your point of view. Robert B. and I
> chatted about this thread when it started, and I think he convinced me
> that the "right" point of view is that RIF is supposed to be a model
> of \mathbb{R} that keeps track of errors for you -- that RIF is a
> drop-in replacement for, say, RDF, and that it keeps track of
> precision as you go. From this point of view, I think there's no
> question of what the behavior of floor() should be.
>
> On the other hand, if you're just thinking of intervals as
> intrinsically interesting objects, maybe this isn't as natural? I
> guess I can just put the ball back in your court: Jason, what do
> intervals mean to you? ;)
I agree with Robert; at least, that is my use-case for using intervals
next semester in teaching numerical analysis.
I speak from a programmatic point of view, though. I'd like to not be
surprised that the following doesn't work:
a=sin(floor(RIF( (1.1,1.2) )))
a.lower()
a.upper()
versus
a=sin(floor(RIF((1.5,2.5))))
a.lower()
a.upper()
In other words, I don't think that the return type of floor() should
depend on how big the interval is.
If you are keeping track of errors, then I think floor(RIF(1.5, 2.5))
should return an interval (possibly a discrete analog, i.e., just the
integers [1,2] in a class that acts like an interval). Thus, I think
that floor(an interval in which all numbers have the same interval)
ought to return an interval, where both endpoints are the same.
Jason
--
Jason Grout
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send an email to sage-devel@googlegroups.com
To unsubscribe from this group, send an email to
sage-devel-unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URL: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
