Detecting cusps and inflection points in curves
The authors call `cusp of order \(k\)' a point on a curve where the \(k\)-th osculating space is not of maximal dimension. \{The underlying theory, not noticed by the authors, of higher order contact and singularities was developed by \textit{W. F. Pohl} [Topology 1, 169-211 (1962; Zbl 0112.366)] and \textit{E. A. Feldman} [Trans. Am. Math. Soc. 20, 185-225 (1966; Zbl 0137.178), ibid. 125, 181-215 (1966; Zbl 0156.424)]\}. The authors note that if a curve is given in parametric form by rational functions the existence of singularities of any order in a given interval can be detected by using Sturm chains.
scientific article; zbMATH DE number 68925