Grobner bases calculations of the paper "Four-dimensional Lorentzian algebraic Ricci solitons"

This notebook is a complementary file for the paper "Four-dimensional Lorentzian algebraic Ricci solitons". It contains the calculations of the Ricci tensor and the polynomial equations which determine the algebraic Ricci solitons for each of the left-invariant metrics in the four-dimensional Lorentzian setting. Moreover, the calculations of the different Gröbner bases used in the paper are also included in the corresponding cases. Headings and numbering correspond to those in this paper.