ICMS 2024 Session

Machine Learning within
Computer Algebra Systems

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Rohit John and James H. Davenport — Machine Learning for Variable ordering in Cylindrical Algebraic Decomposition

Abstract

Cylindrical Algebraic Decomposition is a computer algebra tool with many applications, from robotics to biochemistry. But it can be very sensitive to the ordering of the variables, which may be partially prescribed by the problem, but generally has at least some freedom. There are various algorithmic heuristics to choose the best variable order, some cheap (e.g. Brown's) and some expensive (e.g. ndrr). Much previous research has concentrated on using machine learning to select the most suitable heuristic (which is very often Brown's). We are looking at using machine learning heuristics to pick the variable order directly. Of those machine learning methods we have currently implemented, Feed Forward Networks seem the most successful (though others are nearly as good), and much better than Brown's.