Researchers

Dr. Shawki. M. AL Rashed

Published in

Damascus University Journal of Basic Sciences, Volume 34, Issue 2, 2018.

Abstract

The computation of the local dimension of an algebraic set at a numerical approximation to a point on it depends on the computation of the maximum dimension of irreducible components of the algebraic set, which pass through this point. Depending on some theorems and properties in the algebraic geometry and in commutative algebra we modified the algorithms [2] in and in [5] to compute local dimension by using less steps of Homotopy functions than it is in [5] by starting at a number less than the number of the variables and without the use of the concepts "Triangular Set", Witness Point Sets, and the continuation of the Homotopy function as in [2].

Key words:   local dimension, algebraic set, Krull's dimension, Groebner Bases, square form, Homotopy function.

Link to read full paper

http://damascusuniversity.edu.sy/mag/asasy/FCKBIH/file/2-2018/185-202.pdf