Given a Polynomial of degree with roots , , ..., and a Polynomial of degree
with roots , , ..., , the resultant is defined by

There exists an Algorithm similar to the Euclidean Algorithm for computing resultants (Pohst and Zassenhaus 1989). The resultant is the Determinant of the corresponding Sylvester Matrix. Given and , then

is a Polynomial of degree , having as its roots all sums of the form .

**References**

Pohst, M. and Zassenhaus, H. *Algorithmic Algebraic Number Theory.*
Cambridge, England: Cambridge University Press, 1989.

Wagon, S. *Mathematica in Action.* New York: W. H. Freeman, p. 348, 1991.

© 1996-9

1999-05-25