The main problem of designing augmented systems or minimally extended systems for the numerical computation of singular points is to find appropriate conditions depending on the type of singular point such that the singular point becomes a regular solution of the inflated system. For the reduced problem, i.e. for the problem after having applied the Lyapunov-Schmidt reduction, this task is solved in singularity theory in form of recognition theorems. In the present paper, we show that there is a constructive transcription rule which allows to carry over these results to the original problem thus giving an explicit way how one can design augmented and minimally extended systems. @ –x