Polynomial Index

The index of a polynomial P(x1,x2, ..., xk) at a point q = (q1, q2, ..., qk) is defined as follows:
Let a1, a2, ..., am be he distinct real roots of P(q1,q2, ..., q(k-1),xk), in ascending order. Let a0 be minus infinity and a(m+1) be plus infinity. Let i be the unique index such that qk is in [ai,a(i+1)). The index of P in q is 2i if ai = qk, and 2i + 1 otherwise.

Christopher W. Brown
Last modified: Fri Jun 26 14:56:11 EDT 1998