### Mathematical definition

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

| (55)

where , while is obtained by solving

| (56)

and are chosen such that the matrix in (56) is nonsingular. An advantage of this method is that the derivatives of can be obtained easily from the derivatives of :

where is a state variable or an active parameter and w is obtained by solving

| (57)

This method is implemented in the curve definition file `limitpoint.m`.