#11506: Fix the infinity ring.
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Reporter: vbraun | Owner: AlexGhitza
Type: defect | Status: needs_info
Priority: blocker | Milestone: sage-6.3
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Volker Braun | Reviewers: Peter Bruin
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vbraun/infinity_ring | 3531287276d95f0a60b762c4dc5475bee4860cba
Dependencies: 13125 | Stopgaps:
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Comment (by pbruin):
Replying to [comment:29 vbraun]:
> If anything it is about more coarse approximation, this is why there is
a coercion RR -> signed infinity -> unsigned infinity.
It is more coarse to certain extent; on the other hand `RIF` does not in
general specify whether an element is positive, negative, zero, plus or
minus infinity.
> There is also a coercion RR -> RIF. IMHO there ought to be a pushout,
and right now its the infinity ring. Arguably it should be a better
structure that also knows about semi-infinite intervals.
Indeed, something like a `InfinityIntervalRing` (although we may want a
less silly name); its elements should be intervals in the ordered set
{{{
-infinity < -finite < 0 < +finite < +infinity
}}}
> Really, the only question right now is whether unbounded intervals ought
to coerce into a finite number or infinity. The convention that I chose is
where
> {{{
> sage: RIF(0,oo) == oo == RIF(0,oo).center()
> True
> }}}
> Do you really want `RIF(0,oo) < oo == RIF(0,oo).center()`? Because that
is the only alternative.
Would there be anything against not trying to implement conversion `RIF`
-> `InfinityRing` in this ticket at all (i.e. letting it raise an error
like it does now), and fix comparison in a better way (and on a different
ticket) by implementing this "infinity interval ring"?
Conversion from `RIF` to the current `InfinityRing` is already broken
anyway, even when there are no infinities involved; do you convert the
interval [-1, 1] into "a negative finite number", "zero", or "a positive
finite number"?
--
Ticket URL: <http://trac.sagemath.org/ticket/11506#comment:30>
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