Hi,
Sage happily coerces floating-point numbers (e.g., elements of RR) into
intervals (e.g., elements of RIF), subject to some conditions on the
precision of the source and destination rings.
The relevant portion of the coercion graph looks like this:
( +---> RDF )
| |
Exact v
real ---> RLF ---> RR
fields |
| v
+---> RIF
The coercions RLF --> RIF and RLF --> RR --> RIF violate the requirement
that coercions should form a commutative diagram. Right now, it is not
too much of an issue in practice, because coercions X --> RIF are
constructed based on the existing coercions X --> RR and direct
coercions like RLF --> RIF always(?) end up being preferred to variants
going through RR.
But this is of course pretty fragile to changes in the coercion system.
If a coercion path of the form X --> RR --> RIF is ever chosen for some
exact ring X (whose elements are not exactly representable by elements
of RR!), arithmetic operations between elements of X and intervals will
yield mathematically incorrect results. Besides, things like
sage: iv = 1 + 2^(-55) + 0. + RIF(1)
sage: iv.lower(), iv.upper()
(2.00000000000000, 2.00000000000000)
can already make for subtle bugs in the current situation.
The same issue exists for CC, CIF and friends.
I see little value in having mixed operations between floating-point
numbers and intervals work automatically, so I would be in favor of
removing the coercions from floating-point rings to interval rings
altogether. What do you think?
--
Marc
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