#11506: Fix the infinity ring.
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Reporter: vbraun | Owner: AlexGhitza
Type: defect | Status: needs_review
Priority: blocker | Milestone: sage-6.3
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Volker Braun | Reviewers: Peter Bruin
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vbraun/infinity_ring | cd9242959af9fda6d5351f8410889b36d6b6a392
Dependencies: 13125 | Stopgaps:
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Comment (by pbruin):
I mostly agree with the changes made; they fix some bugs and don't seem to
introduce new weirdness.
I still don't believe that `Infinity in RR` is a good thing; I don't think
the arguments for it are strong enough to justify what to me feels like a
huge pain in the eye. But it's not too directly related to the other
points addressed in this ticket, so let's leave it at that for now.
Also, in my opinion, having one complex infinity for each argument is
really just as arbitrary as the current situation of having complex
infinities where the real and imaginary parts can each be a real number,
or positive or negative infinity. But this too is something for another
time.
Now here is something that to me looks like a bug even if you believe that
`RR` should contain `+Infinity` and `-Infinity`:
{{{
sage: unsigned_infinity in RR
True
}}}
This is because of the following two circumstances:
`RR(unsigned_infinity)` is defined (as `RR(infinity)`, to be precise), and
`RR(infinity) == unsigned_infinity` returns True. I would prefer making
`RR(unsigned_infinity)` raise an error, if this can be done without
breaking too much.
And here is a strange inconsistency:
{{{
sage: unsigned_infinity - oo*i
...
ValueError: oo - oo not defined
sage: unsigned_infinity + oo*i
Infinity
}}}
I think this is best resolved by making the second example raise a
`ValueError` like the first one; it seems to me that neither addition nor
subtraction makes sense in the unsigned infinity "ring".
--
Ticket URL: <http://trac.sagemath.org/ticket/11506#comment:19>
Sage <http://www.sagemath.org>
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