Framework for Generating Integrable Expressions

Applications of machine learning are becoming more prominent in the field of computer algebra. Examples of such applications include selecting S-pairs in Buchberger’s algorithm or solving integrals and differential equations directly. With many of these applications, data must be generated to train a model. Methods such as generating binary trees representing mathematical expressions or created randomly in a recursive manner from a set of available function symbols, variables and constants have been discussed. However, these generated expressions do not represent a realistic dataset that draws from the typical Maple user’s experience.

I propose a framework for generating valid mathematical expressions. More precisely, the focus will be on integrable expressions. The difference from other methods lies in the fact that the data generation method will be based on a test suite of data generated from Maple users. Thus, the new synthetic data will have properties similar to integrable expressions that Maple users would typically try. This data generation method will be used to train machine learning models that make efficient choices algorithm selection problems.