2011/01/13 by Călin-Şerban Bărbat, Bărbat, Călin-Şerban
Mathematics · #13P10 #14Hxx #14Jxx #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13P10 #msc:14Hxx #msc:14Jxx
paper · pdf · doi:10.48550/arxiv.1101.2615
16 pages, 7 figures, Singular example code
arxiv created 2011/01/13 · arxiv updated 2011/01/14
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 √(I) and their dual ideals.