Approximate a Space Curve near a Singular Point (AsymptoticSolve)
The solution curves of a system of polynomial equations can be approximated by Puiseux series near a singular point of the system. This example shows how to obtain such approximations using AsymptoticSolve.
The solution curve of these algebraic equations has a singular point at .
Find the Puiseux series solutions for positive .
Find the Puiseux series solutions for negative .
Compare the approximation (blue curve) with the exact solution (red dashed curve; intersection curve of the surfaces).