Determining Singular Solutions of Polynomial Systems via Symbolic-Numeric Reduction to Geometric Involutive Form
XR.203 (Bâtiment XLIM)
We present a method based on symbolic-numeric reduction to geometric involutive form to compute the primary component and the differential operators for an isolated singular solution of a polynomial ideal. The singular solution can be exact or approximate. If the singular solution is known with limited accuracy, then we propose a quadratic-convergent method to refine it to high accuracy.