#17713: implement GoodRealField with help of continued fractions
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Reporter: rws | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-wishlist
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by mmezzarobba):
Thanks for your explanations! Just some quick comments and questions (I
don't think I will have time to think about all that in detail soon).
* I still don't really understand the difference you are envisioninig
between `RLF` and your `GRR`. Why not just improve `RLF`? Also, what would
be the benefits of storing multiple representatives of a real number? Same
question with `RCF`.
* I also don't see what this all has to do with continued fractions.
* As far as I understand the intention of `SR` (well, not ''all'' of `SR`,
but things like elementary and special functions, limits, etc.) is to
sort-of-model complex variable calculus, and the problems with branch cuts
of analytic functions are bugs.
* There seems to be a weak consensus that an algebraic structure name
”Foo“ in Sage (esp. in parent and category names) means ”Effective Foo”.
None of your real fields (even the exact ones) are ”Fields“ in this sense,
since the zero test is undecidable.
* Regarding names, I think I like `FPR` (or `RFP`) for floating-point
numbers and `IR` for intervals better than what you suggest.
* Using `in RR` to test if something ”is real“ still wouldn't be a good
idea in many cases, since there certainly would still be parents with some
”real“ elements that wouldn't coerce into `RR`.
* The problem with `InfinityRing(NaN)` could simply be solved by adding a
`NaN` element to `InfinityRing`. This makes sense with the current model.
Defining a compactification mechanism may also be a good idea, but then I
guess compactifications should be generic constructions that take any
suitable parent and extend it with one or two points at infinity. In other
words, I doubt we need an `RRbar`, just a `TwoPointCompactification(RR)`
and a corresponding functor that the coercion system could apply to decide
that the universe of `[RR(1), -infinity]` is
`TwoPointCompactification(RR)`.
--
Ticket URL: <http://trac.sagemath.org/ticket/17713#comment:4>
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