#11506: Fix the infinity ring.
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Reporter: vbraun | Owner: AlexGhitza
Type: defect | Status: needs_info
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 | 3531287276d95f0a60b762c4dc5475bee4860cba
Dependencies: #13125 | Stopgaps:
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Comment (by pbruin):
Replying to [comment:37 tscrim]:
> So IMO it still is a field (it also is in the category of `Fields`)
`RIF` is definitely not a field (and neither are `RR` and `RDF`). They
are Sage objects that approximate the field '''R''' of real numbers in
different ways, but none of these Sage objects satisfies the axioms of a
field.
> Now the infinity ring is a actually a semiring, but nevertheless it
still has less structure.
I don't understand this. Addition of `+Infinity` and `-Infinity` is
undefined in the infinity ring, or is this what you mean by "less
structure"?
> Even if we don't want to consider which category, the basic promise of
coercion is that if you can do operation `#` on (2 elements of) `A`, then
you can do the same (equivalent?) operation on `B`.
No, the operation `4 // 2` is defined in `ZZ`, but not after coercion to
`Zmod(8)`, for example.
--
Ticket URL: <http://trac.sagemath.org/ticket/11506#comment:38>
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