#18595: Big Oh terms and equality
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Reporter: behackl | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: commutative algebra | Resolution:
Keywords: powerseries, asymptotics | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Replying to [comment:5 behackl]:
> And finally: what about the following:
> {{{
> sage: O(x) == O(x^2)
> True
> }}}
> Does this equality make sense to you?
Yes: the two "intervals" (neighbourhoods is perhaps a better term)
overlap, so they could be representing the same element.
The advantage of this lax form of equality is that if you do computations
with sufficient precision to tell all distinct elements you'll encounter
apart, then you can use the conventional algorithms to arrive at an
answer. That means that you can for instance do linear algebra with power
series using normal tools, provided you start with enough precision. This
works fairly well in practice and you'll usually discover a catastrophic
loss of precision by not having any terms left. Of course, for serious
applications you do have to use proper numerical methods anyway, but then
you won't be using equality tests anyway.
--
Ticket URL: <http://trac.sagemath.org/ticket/18595#comment:6>
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