guessing formulas for sequences

[mantepse]

Given the initial terms of a sequence of numbers (or polynomials or whatever) we want to find a differential or algebraic or functional equation for the generating function or a explicit formula for the individual terms.

TODO: a couple examples

    sage: guess(....)
    ....

TODO: links to existing implementations

Depends on #15714
Depends on #16008

CC: @sagetrac-sage-combinat @rwst @mezzarobba

Component: combinatorics

Issue created by migration from https://trac.sagemath.org/ticket/11515

[rwst]

comment:1

This can mean several things:

• a guesser of sequences generated by rational polynomials (linear recurrences with constant coefficients), dependent on
  1. the ring of such recurrences
• a guesser of sequences generated by holonomic functions (P-finite sequences, recurrences with coefficients being polynomials in the sequence index n), dependent on
  1. the ring of such recurrences
• guessers for other types of sequences

So this issue depends on several sub-issues.

[rwst]

Dependencies: #15714

[rwst]

Changed dependencies from #15714 to #15714, #16008