Several Methods For Computing The Resultant And Its Applications

Computational methods for manipulating sets of polynomial equations are becoming of greater importance due to the use of polynomial equations in various applications. Recently, the techniques of Groebner bases and polynomial continuation have become the main computing methods. But when it comes to practice, these methods are slow and not effective for a variety reasons. In this paper we introduce the resultant and its efficiency for manipulating system of polynomial equations. We conclude research findings about resultant theory systematically, not only introduce some methods for computing the resultant which include a better method -remainder method, but also expatiate the widely applications of resultant, especially in the eliminate theory , and we extend some resultant theory into n-tuples situation, namelyconstructing 1,2,L ,n-1 orders resultant to resolve the n-tuples non-linear algebraic equations.