A Survey on the Use of Machine Learning within Computer Algebra

Abstract

This survey explores the use of Machine Learning (ML) in the field of Computer Algebra (CA), both to optimise existing CA algorithms, and to perform symbolic computation directly. Traditional symbolic methods, while mathematically rigorous, often are computationally expensive thus limiting their use in real-world applications. Recent advances have shown that data-driven techniques can address these limitations by guiding heuristic decisions, selecting optimal algorithms, predicting structural properties of algebraic objects, or even making direct symbolic computations. We take a systematic literature review approach and uncover work in CA applications including cylindrical algebraic decomposition, Gröbner basis computation, symbolic integration, and many more. The survey compares the different ML approaches that have been employed for these tasks, ranging from decision trees to transformers. Issues uncovered by the survey include the lack of benchmark datasets for CA, which hinders the comparison of methods and the generalizability of ML models. The survey identifies the potential for explainable AI tools to help develop trust in decisions, and to drive forward CA research itself.