Resultants and Subresultants

In this chapter we shall study resultant, an important and classical idea in constructive algebra, whose development owes considerably to such luminaries as Bezout, Cayley, Euler, Hurwitz, and Sylvester, among others. In recent time, resultant has continued to receive much attention both as the starting point for the elimination theory as well as for the computational efficiency of various constructive algebraic algorithms these ideas lead to; fundamental developments in these directions are due to Hermann, Kronecker, Macaulay, and Noether. Some of the close relatives, e.g., discriminant and subresultant, also enjoy widespread applications. Other applications and generalizations of these ideas occur in Sturm sequences and algebraic cell decomposition—the subjects of the next chapter.