ICMS 2020 Session

Real Algebraic Geometry

Accepted Talk

Li-Yong Shen (University of the Chinese Academy of Sciences, Beijing)
A Maple package for implicitization of rational curves and surfaces
Abstract: Implicitization is a classic problem in computer algebra and computer aided geometric design. We propose a software package, Implicit, that contains several popularly used functions related to the implicitization of rational curves and tensor product surfaces. Two main functions ImpCurve and ImpSurface are designed for implicitizing a rational planar curve and a rational tensor product surface. ImpCurve is based on the moving line technique for implicitizing rational curves mu-basis, which has shown its great advantage in computational efficiency. ImpSurface is developed according to the recent developments on surface implicititzation methods by an automatic checking process. This method essentially combines three techniques including the Dixon A-resultant, the moving plane and moving quadric technique, and the resultant of simple syzygies, morevoer, for implicitizing rational ruled surfaces the function will choose a more efficient way only by univariate resultant. The ImpSurface will return the implicit equations automatically if it succeeds. However, we also propose subfunctions ImpbyDixonA, Impbympmq, Impby3mp and ImpRuled for the user to test the details of the implicitization methods.