2007/07/02 by David A. Weinberg, Weinberg, David A., Nicholas J. Willis +1
Computer Science · Engineering · Mathematics · #14B05 #14Bxx #14H20 #14Hxx #32Sxx #58Kxx #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0707.0241
openalex publication_date 2007/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are thirteen types of singular points for irreducible real quartic curves and seventeen types of singular points for reducible real quartic curves. This classification is originally due to D.A. Gudkov. There are nine types of singular points for irreducible complex quartic curves and ten types of singular points for reducible complex quartic curves. We derive the complete classification with proof by using the computer algebra system Maple. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. Thus, the proof consists of a sequence of large symbolic computations that can be done nicely using Maple.