`recurrence-guess.gp`

This is a spot of Pari/GP code to guess a linear recurrence from a vector of numbers (or even from polynomials for guessing with a symbolic parameter). If successful the result is pretty printed. For example,

recurrence_guess([1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609]); => Recurrence length=3 Coefficients v[n-3]* [4, -8, 5] *v[n-1] = v[n] v[n] = v[n-1]* [5, -8, 4] *v[n-3] Characteristic polynomial x^3 - 5*x^2 + 8*x - 4 = factors (x - 2)^2 root 2.00000 x - 1 root 1.00000 Generating function (1 - 2*x + 2*x^2)/(1 - 5*x + 8*x^2 - 4*x^3) = partial fractions 1/(1 - x) - 1/(1 - 2*x) + 1/(1 - 2*x)^2 As powers n * 2^n + 1

The guess is found by a simple `matsolve()`

. Linear recurrences
include powers, polynomials, and polynomials times powers. Similar code can
be found in
`findrec()`

by Charles R. Greathouse and
`ggf()`

in the OEIS
Sequence Tools. Bill Allombert points out too that
`bestapprPade(Ser(vec))`

gives a generating function. The nice display here in various forms is the
tedious part. Of course "nice" is a matter of personal preference and the
output is still quite mechanical.

`recurrence-guess.gp`

is
free software (free
as in freedom), published under the terms of the
GNU
General Public License (v3 or higher). Download version
7 here. Requires my
`pol-pfrac.gp`

.

`recurrence-guess.gp`

(43k, and sig)

`recurrence-guess-7.tar.gz`

(39k, and sig)

Just `recurrence-guess.gp`

and
`pol-pfrac.gp`

are
enough to run. The `tar`

file includes some self-tests. The sig
files are Gnu PG ascii armoured signatures
generated from my key.

This page Copyright 2016, 2017 Kevin Ryde, except for the GPLv3 logo which is Copyright Free Software Foundation and used here in accordance with its terms.

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