# Algorithmically generating new algebraic features of polynomial systems for machine learning

arXiv: https://arxiv.org/abs/1906.01455 · HTML: https://mlsanity.com/paper/1906.01455/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2019.

## Built on by (most cited first, 6 of 6)

- [Explainable AI Insights for Symbolic Computation: A case study on selecting the variable ordering for cylindrical algebraic decomposition](https://mlsanity.com/paper/2304.12154/) (2023)
- [Data Augmentation for Mathematical Objects](https://mlsanity.com/paper/2307.06984/) (2023)
- [Lessons on Datasets and Paradigms in Machine Learning for Symbolic Computation: A Case Study on CAD](https://mlsanity.com/paper/2401.13343/) (2024)
- [Constrained Neural Networks for Interpretable Heuristic Creation to Optimise Computer Algebra Systems](https://mlsanity.com/paper/2404.17508/) (2024)
- [SC-Square: Future Progress with Machine Learning?](https://mlsanity.com/paper/2209.04361/) (2022)
- [Breaking the Data Barrier in Learning Symbolic Computation: A Case Study on Variable Ordering Suggestion for Cylindrical Algebraic Decomposition](https://mlsanity.com/paper/2601.13731/) (2026)

## Abstract (arXiv)

There are a variety of choices to be made in both computer algebra systems (CASs) and satisfiability modulo theory (SMT) solvers which can impact performance without affecting mathematical correctness. Such choices are candidates for machine learning (ML) approaches, however, there are difficulties in applying standard ML techniques, such as the efficient identification of ML features from input data which is typically a polynomial system. Our focus is selecting the variable ordering for cylindrical algebraic decomposition (CAD), an important algorithm implemented in several CASs, and now also SMT-solvers. We created a framework to describe all the previously identified ML features for the problem and then enumerated all options in this framework to automatically generation many more features. We validate the usefulness of these with an experiment which shows that an ML choice for CAD variable ordering is superior to those made by human created heuristics, and further improved with these additional features. We expect that this technique of feature generation could be useful for other choices related to CAD, or even choices for other algorithms with polynomial systems for input.