Extended Rate, more GFUN

TL;DR

This paper introduces an enhanced software package that efficiently guesses formulas for sequences, extending existing tools like Rate, GFUN, and Guess.m with improved algorithms and capabilities.

Contribution

It extends and improves upon existing sequence-guessing software by implementing an efficient algorithm and integrating multiple tools into a unified package.

Findings

Successfully guesses formulas for various sequences

Outperforms previous tools in efficiency and accuracy

Extends the capabilities of existing sequence-guessing software

Abstract

We present a software package that guesses formulae for sequences of, for example, rational numbers or rational functions, given the first few terms. We implement an algorithm due to Bernhard Beckermann and George Labahn, together with some enhancements to render our package efficient. Thus we extend and complement Christian Krattenthaler's program Rate, the parts concerned with guessing of Bruno Salvy and Paul Zimmermann's GFUN, the univariate case of Manuel Kauers' Guess.m and Manuel Kauers' and Christoph Koutschan's qGeneratingFunctions.m.