### Mathematical definition

In the toolbox branch point curves are computed by minimally extended defining systems, cf. [22], §4.1.2. The branch point curve is defined by the following system

| (81)

where , while and are obtained by solving

| (82)

Here and are functions and and are scalars and

where the bordering functions and scalars are chosen so that is nonsingular. This method is implemented in the curve definition file `branchpoint.m`.