The Triangularization For Polynomial Systems With Applications In Differential Equations Based On An Algorithm Of Real Root Isolation

Triangular decompositions for polynomial systems play a key rolein solving systems of polynomial equations and in constructing small amplitudelimit cycles. Wu's method, one of the important methods of triangularizing poly-nomial systems, tells us that the triangularization for polynomial systems canbe accomplished by the successive pseudo division of polynomials. By modify-ing Wu's method, a new technique of triangularization for polynomial systems isdeveloped, which is able to avoid the possible explosion of polynomials to someextent by decreasing the computational complexity.An algorithm of real root isolation for polynomial systems is one of themethods to solve systems of polynomial equations. Based on the estimates ofabsolute values of the roots, Role theorem, Sturm sequence, and Descartes'ruleof sign, intervals containing a real root can be obtained by the algorithm. Abrief introduction of the algorithm for isolating real roots of multivariate integralpolynomial systems is provided in Chapter one.Chapter two presents the process and the algorithm of the modified methodof triangularization for polynomial systems. By employing Wu's method and themodified technique, an example is provided to show that the latter method seemsto be more efficient for seeking one required solution which ensures initials to benonzero.By applying the modified technique , a kind of large initials which is hardlyto be expanded as the rational functions of the variables is likely to be produced.