Canonical reference on applied elimination theory? I would like to study elimination theory as it is applied to sets of multivariate polynomials. I am interested in cases where some variables are completely eliminated, as well as cases where higher degree monomials are eliminated and the number of variables preserved. Does anyone know of a canonical reference book that concentrates on applications? Thank you for any suggestion! 

Elimination theory is a quite classical topic, and there are many books covering the main arguments.
Since you seem to be intersted in computations and applications, I surely recommend you the really nice books Using algebraic geometry and Ideals, varieties and algorithms, both by Cox, Little and O'Shea
