# Procedures

Here is a diagram illustrating the algorithmic structure of the classical Borcherds’ method, which involves most of the above-mentioned procedures : Assume that the Borcherds’ method accomplished its $k$-th iteration. Denote by $\mathcal{L}_k$ the set of chambers of level $k$ each representing their own congruence class of chambers and identified during the $k$-th iteration.

The Poolized Borcherds’ method is a modernized version of the Borcherds’ method which fully takes advantage of process-based parallelism :