#16137: lazy_list from various input data
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Reporter: MatthieuDien | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: misc | Resolution:
Keywords: LazyPowerSeries, lazy_list, | Merged in:
days57 | Reviewers:
Authors: Vincent Delecroix, Matthieu | Work issues:
Dien | Commit:
Report Upstream: N/A | Stopgaps:
Branch: |
Dependencies: |
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Old description:
> The current `sage.misc.lazy_list` only dealt with infinite list built
> from iterator.
> In concrete situation we want to create infinite list from :
> - '''an iterator'''
> - '''an update function''': a function that given a buffer of already
> computed values compute some extra terms. This includes closed forms
> (i.e. a function n -> n-th term) and algorithms that compute many terms
> at a time (e.g. in the context of words: fixed point of substitutions and
> in the context of power series: Newton iteration and relaxed
> multiplication)
> - '''a pair of lists (pre-period,period)''' that defines an ultimately
> periodic infinite sequence
> Those new lazy lists aim to be very basic Python objects. Their purpose
> is to be used as fast and reliable data structure in:
> - words (`sage.combinat.words`)
> - continued fraction expansions/binary expansions of real numbers
> - lazy power series (see #15673)
> - ...
>
> See also: rational o.g.f. #15714, hypergeometric e.g.f. part of #2516
New description:
The current `sage.misc.lazy_list` only deals with infinite list built from
iterator.
In concrete situation (as in #15673) we want to create infinite list from
:
- iterator
- a function that given `n` computes the `n`-th term (also called closed
form)
- a function which updates a buffer of already computed values (for
example : Newton iteration, relaxed multiplication, ...)
- an ultimatey periodic list (from a pre-period and a period)
- entries generated by functions (rational o.g.f. #15714, hypergeometric
e.g.f. part of #2516)
--
Comment (by rws):
I am aware that it looks like we would only look at numbers. But I was
only listing what is already available in code. I would like to have an
overview of the hierarchy you mention, not the least because it would help
with the design of the code planned here. Where could such an overview (of
the hierarchy of formal power series and sequences) be found?
--
Ticket URL: <http://trac.sagemath.org/ticket/16137#comment:8>
Sage <http://www.sagemath.org>
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