#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 tscrim):
There should be a bit better check of equality in RIF as `x - x` will be 0
because we know we are subtracting the same number (even if we don't know
the exact number). However `RIF(0,1) - RIF(0,1)` may or may not be 0, we
don't know because the left and right terms may or may not be the same
value. So IMO it still is a field (it also is in the category of
`Fields`), but doing exact comparisons can be difficult.
Now the infinity ring is a actually a semiring, but nevertheless it still
has 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`.
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Ticket URL: <http://trac.sagemath.org/ticket/11506#comment:37>
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