On Wed, Mar 11, 2009 at 9:35 PM, Robert Bradshaw
<rober...@math.washington.edu> wrote:
>> Here's some examples to hopefully clarify:
>
>
>> RealField(20) -> RealField(50)
>> RealField(20) -> RealIntervalField(20)
>
> I would call these dangerous, as the latter implicitly has more
> "information" than the former.

No they don't:

sage: pi20.exact_rational()
411775/131072
sage: RealField(50)(pi20).exact_rational()
411775/131072

See, exactly the same information :)

Remember that in my proposal, these "safe" coercions/conversions (I
said I needed a better name!) are only used for comparisons and "in".
The effect is that since RealField(20)->RealField(50) is a safe
conversion (not a coercion!), and RealField(50)->RealField(20) is an
unsafe coercion, RealField(20)(pi)==RealField(50)(pi) would return
False.  (I want this behavior a lot more often than I want the current
behavior, where this equality test gives True.)

Carl

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