Hi Marco,
I read that comment, but it looks like the coercion framework does what it
> should. RR(oo) == oo is evaluated by coercion to InfinityRing, where
> positive infinity equals positive infinity:
>
> sage: oo
> +Infinity
> sage: oo.parent() is InfinityRing
> True
> sage: InfinityRing.has_coerce_map_from(RR)
> True
>
Right, from that perspective it is hard to argue that there is a bug.
> As far as I can see, to make RR(oo) == oo evaluate to False (or give an
> error), while staying consistent with the coercion framework, one would
> need to either
> - disallow the explicit conversion RR(oo), or
> - remove the automatic coercion from RR to InfinityRing, or
> - make InfinityRing(RR(oo)) finite.
>
The only two options that seem acceptable to me are
- disallowing RR(oo) (if RR is taken to represent the field of real numbers
as opposed to the extended real line);
- making the "in" keyword treat infinity as a special case. This could be
defended by saying that representing infinity in RR or CC is possible for
convenience, but should not be viewed as an instance of set-theoretical
containment. I think this is similar to saying that +0.0 and -0.0 are
represented differently in our implementation of floating-point arithmetic,
but should be regarded as equal by comparison operators.
The following all make sense and look useful:
>
> sage: UnsignedInfinityRing.has_coerce_map_from(RR) # natural map RR -->
> {finite, infinite}
> True
> sage: UnsignedInfinityRing.has_coerce_map_from(CC) # natural map CC -->
> {finite, infinite}
> True
> sage: InfinityRing.has_coerce_map_from(RR) # natural map RR --> { -oo,
> negative, 0, positive, +oo}
> True
> sage: InfinityRing.has_coerce_map_from(CC) # no natural map CC --> { -oo,
> negative, 0, positive, +oo}
> False
>
Yes, I cannot think of any reason to change this.
Peter
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