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.