The quadratic (Pfaffian) relations define a complete intersection variety $Q$ in a $\mathbb{P}^n$ of $a$-variables. In this procedure, we compute the loci of points in $Q$ at which the rank of $e$-matrix drops, that is, the minimal primes of the maximal minors of the $e$-matrix (within the variety $Q$). These loci play an important role for the construction of surfaces with torsion groups $\mathbb{Z}/n\mathbb{Z}$ for $n \geq 3$.
The object lowerRankLociE is a method function.