We use machine learning to verify and predict the solution distribution of some simple polynomial equations defined over a finite field.
- distribution.ipynb: original analysis by Xiyuan Wang
- Sato-Tate.ipynb: some improved analysis and additional hypothesis testing results by Fei Xie
- Sato-Tate_hyperelliptic.ipynb: follow Fei Xie's analysis, did some experiments on hyperelliptic curves by Xiyuan Wang
We enumerated rational points on a hyperelliptic curve over a large range of finite fields and verified Sato-Tate conjecture by Kolmogorov–Smirnov test from statistics. Along the way, we also applied machine learning techniques ranging from Linear regression, gradient boosting Decision tree to Neural networks.