#### Document Type

Article

#### Publication Date

2009

#### Abstract

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. There are 42 types of real singular points for irreducible real quintic curves and 49 types of real singular points for irreducible real quintic curves. The classification of real singular points for irreducible real quintic curves is originally due to Golubina and Tai. There are 28 types of singular points for irreducible complex quintic curves and 33 types of singular points for reducible complex quintic 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 cam be done nicely using Maple.

#### Recommended Citation

Weinberg, David A. and Willis, Nicholas J., "Singular Points of Real Quartic and Quintic Curves" (2009). *Faculty Publications - Department of Mathematics and Applied Science*. 4.

https://digitalcommons.georgefox.edu/math_fac/4

## Comments

Originally published by

Tbilisi Mathematical Journal, Volume 2, 2009, p. 95-134.http://www.tcms.org.ge/Journals/TMJ/