ELIMINATION THEORY AND ITS APPLICATIONS

Abstract

This project report will focus on various methods for finding the solutions of system of polynomial equations . There are two main theorems- The Elimination Theorem and Extension Theorem for getting the solutions of the system of equations . First, we will study about the above theorems using the concept of Grobner Basis. Second, we will discuss about the geometric interpretation of elimination when we will discuss the Closure Theorem. In context of the applications of elimination theory , we will discuss two in detail: Implicitization problem and envelope of family of curves.