The BKK root count in ๐โฟ
Taiyong Li, Xiaoshen Wang ยท Mathematics of Computation ยท 1996
The root count developed by Bernshtein, Kushnirenko and Khovanskii only counts the number of isolated zeros of a polynomial system in the algebraic torus ( C โ ) n (\mathbf {C}^*)^n . In this paper, we modify this bound slightly so that it counts the number of isolated zeros in C n \mathbf {C}^n . Our bound is, apparently, significantly sharper than the recent root counts found by Rojas and in many cases easier to compute. As a consequence of our result, the Huber-Sturmfels homotopy for finding all the isolated zeros of a polynomial system in ( C โ ) n (\mathbf {C}^*)^n can be slightly modified to obtain all the isolated zeros in C n \mathbf {C}^n .