On Coxeter spectral study of finite posets using computer algebra tools

We study a class of posets with a non-negativity condition by means of Coxeter spectral properties of the simply-laced Euclidean diagrams . We show that symbolic and numerical computer calculations in Python, C and Linux tools allow us to compute a complete list of these posets J, with at most 15 points, by means of their Coxeter spectra speccJ⊆C.