Applying a Computational Algebra and Data Science Pipeline to Clifford Algebra and Cluster Algebra Data

We present a paradigm and pipeline to explore algebraic data sets using data science methods such as exploratory data analysis, neural networks, gradient saliency, and principal component analysis. This is achieved by coupling standard machine learning approaches with computational algebra methods, either in an enumerative or a shotgun way. This is exemplified by two examples of algebraic data: in Clifford algebra, a certain emerging type of interesting invariants of linear functions, which we choose to be the Coxeter elements of ADE type in dimension 8 as a concrete example. We also provide some novel analytical results for these cases. The other example is that of different types of algebraic data of interest in a cluster algebra context. For completeness, we also signpost to a similar approach for simulated data in a computational biology context concerning virus assembly. This approach points to a new computer-aided paradigm for exploring mathematical structures, building intuition, formulating hypotheses, and proving novel theorems.