Dualization of projective algebraic sets by using Gr\"obner bases elimination techniques
Abstract
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 Gr\"obner bases method. A dualization algorithm is implemented in the computer algebra system Singular. Some examples are given. The main diagram shows the relationship between the ideal I, its radical I and their dual ideals.
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