An Algorithm For Isolating Real Roots Of Rational Polynomial Systems And An Algorithm For Calculating Liapunov Values Of Polynomial Li?nard Systems

Solving systems of (symbolic or numerical) polynomial equations in several variables has been a very important topic for theoretical oriented research groups.In Chapter One , based on the characteristic set method, real root isolation algorithm and the evaluation for maximal and minimal polynomials, we propose an algorithm for isolating real roots of multivariafe rational polynomial systems.This algorithm is an extension of real root isolation algorithm for univarioie rational polynomial. It results in an higher-dimensional isolated interval for each isolated real root.In the ordinary differential equation qualitative or stability analysis, Lienard systems are typical. Now, there are many researches on the numbers of their small amplitude limit cycles. In Chapter Two, we give out an algorithm for calculating the Liapunov values of polynomial Lienard systems. By using the algorithm, we consider the numbers of small amplitude limit cycles of several special polynomial Lienard systems.