Elimination theory

Summary

Elimination theory studies how to remove some variables from a system of polynomial equations, so as to obtain the equations satisfied by the remaining variables. Its basic object is the elimination ideal, the set of consequences of the system that involve only the remaining variables. Classical tools are resultants; the modern tool is a Gröbner basis for a lexicographic order. Geometrically, elimination computes the closure of the projection of the solution set to fewer coordinates.