MANPAK: a set of algorithms for computations on implicitly defined manifolds

Mathematical models often involve differentiable manifolds that are implicitly defined as the solution sets of systems of nonlinear equations. The resulting computational tasks differ considerably from those arising for manifolds defined in parametric form. Here a collection of algorithms is presented for performing a range of essential tasks on general, implicitly specified submanifolds of a finite dimensional space. This includes algorithms for determining local parametrizations and their derivatives, and for evaluating quantities related to the curvature with sensitivity measures. The methods have been implemented as a FORTRAN 77 package, called MANPAK.