Concerning the software used to deal with nonlinear systems of equations (their generation or their resolution), the following products appear in almost all the answers.
In general, but not always, Symbolic and Numeric software such as Matlab is
either used in a first stage during the preprocessing of the modelling
equations, or as a checking procedure which provides a simulation of
how the software which comprises the final solution should behave.
It is worth mentioning that in
several cases (for example, for the tolerance analysis in the design of a
variational CAD/CAE system at LABEIN), some subroutines from the NAG or IMSL
libraries are incorporated in the final product. In other cases a less sophisticated, but also useful, solution comes from using the `` Numerical Recipes" book (in the design of a CAD system at CANDEMAT).