Approximate a Plane Curve near a Singular Point (AsymptoticSolve)
The solution curves of a polynomial equation 
can be approximated by Puiseux series 
near a singular point 
of the equation. This example shows how to obtain such approximations using AsymptoticSolve.
The solution of this algebraic equation has a singular point at 
. Near singular points, algebraic curves can be approximated by Puiseux series.
Find the Puiseux series solutions for positive 
.
Find the Puiseux series solutions for negative 
.
Compare the approximations with the exact curve.
show complete Wolfram Language input
