#18709: closed forms of C-finite sequences
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Reporter: rws | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: commutative | Resolution:
algebra | Merged in:
Keywords: | Reviewers:
Authors: Ralf Stephan | Work issues:
Report Upstream: N/A | Commit:
Branch: | f643cb401dec648fe0bc601573a5b019d58676ea
u/rws/closed_forms_of_c_finite_sequences| Stopgaps:
Dependencies: |
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Comment (by vdelecroix):
Replying to [comment:5 rws]:
> Vincent, you probably read the word `fibonacci`, but did you notice that
in `binary_recurrence_sequences.py` only a small part of C-finite
sequences is treated, ie those of degree 2? Have you noticed that our
implementation can guess a sequence from the numbers? And with this ticket
you get a closed form for immediate and fast evaluation of any binary or
other recurrence.
I have enough mathematical background to know that binary means two.
Recurrence of degree 2 is a particular case and this is why it may have
been a ''starting point'' for general linear recurrence sequences. I never
claimed that you redid what was already done. But just that you ignored
other's work.
> As to your question about the ring of C-finite sequences I refer you to
> {{{
> .. [Z11] Zeilberger, Doron. "The C-finite ansatz." The Ramanujan Journal
> (2011): 1-10.
> }}}
The word ring is not in the article... could you give more explanations?
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Ticket URL: <http://trac.sagemath.org/ticket/18709#comment:6>
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