Ueber die Bestimmung des Grades einer durch Elimination hervorgehenden Gleichung (On the determination of the degree of an equation obtained by elimination)
Abstract
Description
[Inserted by J. Maurice Rojas] We give a formula for the number of complex roots of a generic system of two polynomial equations in two unknowns. The formula is completely combinatorial, ultimately depending just on the convex hull of the exponent vectors of the equations. This formula presents the first known pre-cursor to David N. Bernstein's theorem relating mixed volumes and the number of roots in the complex algebraic torus of a system of polynomial equations. More precisely, our formula is a special case of a formula derived in 1994 by T. Y. Li and Xiaoshen Wang.
Replica, typed by Mrs. Nishanti, of famous paper 1841 paper of Ferdinand Minding which foreshadowed David N. Bernstein's famous theorem relating mixed volumes of polytopes and algebraic geometry. This paper is in German but a translation (with commentary) by David A. Cox and J. Maurice Rojas is available as math.HO/0310014
Replica, typed by Mrs. Nishanti, of famous paper 1841 paper of Ferdinand Minding which foreshadowed David N. Bernstein's famous theorem relating mixed volumes of polytopes and algebraic geometry. This paper is in German but a translation (with commentary) by David A. Cox and J. Maurice Rojas is available as math.HO/0310014