Gröbner bases calculations of the paper "Conformally Einstein Lorentzian Lie groups: the almost Abelian case"

This notebook is a complementary file of the paper "Conformally Einstein Lorentzian Lie groups: the almost Abelian case". It contains the expressions of the Bach tensor and the calculations of the different Gröbner bases, aimed to provide evidence of the ideal membership of the polynomials used through the paper. Headings and numbering correspond to those in the paper.本笔记本为论文《Conformally Einstein Lorentzian Lie groups: the almost Abelian case》的配套补充文件。其内收录了巴赫张量（Bach tensor）的表达式，以及各类格罗贝纳基（Gröbner basis）的计算过程，旨在为论文中所使用多项式的理想成员问题（ideal membership）提供佐证依据。文中的标题与编号均与该论文保持一致。