The Program CRACK for Solving PDEs in General Relativity

In the introduction an approach to solving differential equations is motivated in which nonlinear DEs are not attacked directly but properties like infinitesimal symmetries or the existence of an equivalent variational principle are investigated. In the course of such investigations over-determined PDE systems are generated, which are to be solved (where the term ‘over-determined’ just stands for ‘more conditions than free functions’). In Sect. 2 algorithms for simplifying and solving over-determined PDE systems are given together with examples. References for more details of the corresponding program CRACK, written by A. Brand and myself, are given.