Recognition of Computationally Constructed Loci

We propose an algorithm for automated recognition of computationally constructed curves and discuss several aspects of the recognition problem. Recognizing loci means determining a single implicit polynomial equation and geometric invariants, characterizing an algebraic curve which is given by a discrete set of sample points. Starting with these discrete samples arising from a geometric ruler and compass construction an eigenvalue analysis of a matrix derived from the data leads to proposed curve parameters. Utilizing the construction itself, with its free and dependent geometric elements, further specifications of the type of constructed curves under generitcity assumptions are made. This is done by a second eigenvalue analysis of parameters of several generically generated curves.