Fri 2018-12-07 13:56:34 UTC+1, Simon King:
> Let x_0 be given, let f be a function defining a sequence (x_0,x_1,...)
> recursively by x_{n+1}=f(x_n).
>
> Is there a tool in Sage that can (at least in sufficiently simple cases)
> deduce a closed formula for x_n? I tried search_def('recurs'), but it
> revealed nothing I could recognise.
There's competition between the words "recursion" and "recurrence",
you might have had more luck with "recurr".
This should be possible using either SymPy, or FriCAS,
or the optional "Ore algebra" package:
http://www.kauers.de/software.html
https://github.com/mkauers/ore_algebra/
Some related discussions can be found through the following queries:
-
https://groups.google.com/forum/#!searchin/sage-devel/ore_algebra%7Csort:date
-
https://groups.google.com/forum/#!searchin/sage-support/ore_algebra%7Csort:date
-
https://ask.sagemath.org/questions/scope:all/sort:activity-desc/page:1/query:ore_algebra/
- https://trac.sagemath.org/query?order=id&desc=1&summary=~ore_a
To highlight some relevant results from sage-devel and sage-support:
- sage-devel, 2016-11
Recurrences and Sequence Formula Guessing Functions in Sage
https://groups.google.com/d/topic/sage-devel/FfJrjaSdkF8/discussion
- sage-support, 2014-09
Formula for simple recursive sequences
https://groups.google.com/d/topic/sage-support/tTqX2BCzjgY/discussion
- sage-devel, 2014-01
class LinearRecurrence
https://groups.google.com/d/topic/sage-devel/PTx12wrVG0c/discussion
- sage-devel, 2013-06
New ore_algebra Sage package is available
https://groups.google.com/d/topic/sage-devel/S7Wv67C6DvE/discussion
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