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 { D ˜ , n ⩾ 4 , E ˜ 6 , E ˜ 7 , E ˜ 8 } . 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 specc J ⊆ C .