Obstructions to genericity in study of parametric problems in control theory: ... The Genericity algorithm is implemented as a procedure genericity in the toolbox control.lib, which is realized as a library in computer algebra system SINGULAR related to control theory. Other support functions are also implemented in the same library. As examples the authors present detailed solutions of the bipendulum equations and “two pendula mounted on a cart” problem, for both negligible friction and essential friction.