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.