Polynomial functions defined over the algebraic structure (R, max, +)
are discussed. All the basic algebraic processes of addition, multipli
cation, evolution and factorisation may be achieved by linear-time alg
orithms. Hence, given an equation of the form Psi(x) = Psi'(x) between
two such polynomials, the extreme points of the solution set, and fin
ally the full solution set, may be determined in linear time.