Guess

Extended rate, more GFUN. We present a software package that guesses formulas for sequences of, for example, rational numbers or rational functions, given the first few terms. Thereby we extend and complement C. Krattenthaler’s program RATE and the relevant parts of GFUN. For some a brain-teaser, for others one step in proving their next theorem: given the first few terms of a sequence of, say, integers, what is the next term, what is the general formula? Of course, no unique solution exists, owever, by Occam’s razor, we will prefer a ‘simple’ formula over a more ‘complicated’ one. In this article we present a new package Guess written for the computer algebra system Axiom. Both Guess and Axiom are freely available and can be tried out online at http://wiki.axiom-developer.org/GuessingFormulas.