  In this note we translate the pictorial description of Gulotta's efficient
inverse algorithm (arXiv:0807.3012) into matrix operations, so that it can be
implemented on a computer. As an application we point out that this in
combination with results from our paper arXiv:0803.3908 provides a fast
algorithm for computing the principal A-determinant of Gelfand, Kapranov and
Zelevinsky for hypergeometric systems in two variables.
