## Singular points of real quartic and quintic curves## David A. Weinberg, Nicholas J. Willis
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 reducible 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 can
be done nicely using Maple.
Tbilisi Mathematical Journal, Vol. 2 (2009), pp. 95-134 |