Dualization of projective algebraic sets by using Gröbner bases elimination techniques
Călin-Şerban Bărbat · arXiv (Cornell University) · 2011
The set of common roots of a finite set $I$ (it is an ideal) of homogeneous polynomials is known as projective algebraic set $V$. In this article I show how to dualize such projective algebraic sets $V$ by elimination of variables from a system of polynomials with the Gröbner bases method. A dualization algorithm is implemented in the computer algebra system {\sc Singular}. Some examples are given. The main diagram shows the relationship between the ideal $I$, its radical $\sqrt{I}$ and their dual ideals.