Making Conjectures about Maple Functions

Abstract

One of the main applications of computational techniques to pure mathematics has been the use of computer algebra systems to perform calculations which mathematicians cannot perform by hand. Because the data is produced within the computer algebra system, this becomes an environment for the exploration of new functions and the data produced is often analysed in order to make conjectures empirically. We add some automation to this by using the HR theory formation system to make conjectures about Maple functions supplied by the user. Experience has shown that HR produces too many conjectures which are easily proven from the definitions of the functions involved. Hence, we use the Otter theorem prover to discard any theorems which can be easily proven, leaving behind the more interesting ones which are empirically true but not trivially provable. By providing an application of HR’s theory formation in number theory, we show that using Otter to prune HR’s dull conjectures has much potential for producing interesting conjectures about standard computer algebra functions.