The Discriminant Systems of Unary Equations and Their Computation

高次方程的判别式系统及其计算

We extend the definition of the discriminant of unary polynomial equations to give a complete description of the multiplicities of the roots of the equations. The method based on Ritt-Wu's decomposition algorithm is constructive. We have given the explicit formulas of all the disciminant systems of polynomial equations whose degrees range from three to five. We also give a description of the invariants of unary equations in terms of the discriminant systems.