UnsignedInfinityRing → SR does not respect the axioms of coercions

[mezzarobba]

Coercions are supposed to be total and transitive, but

sage: SR.coerce(UnsignedInfinityRing(oo))
Infinity
sage: SR.coerce(UnsignedInfinityRing(1))
[...]
NotImplementedError:

See also #17777.

[tscrim]

I think this is an abuse that we have to live with as it is very useful to have this (e.g., to do x + oo).

[mezzarobba]

I more or less agree, but this could bite us in the future, so I thought it may be worth having a place to track the issue and see if we can improve this design.

[mezzarobba]

So, to clarify: I would keep this issue open as minor/wishlist, but feel free to close it if you prefer.

[tscrim]

I think it is good to have this documented as an open issue, and it would be nice to avoid this abuse.