一类平面多项式微分系统赤道环量的代数递推公式

Algebraic Recursion Formulas for Quantities of Equator in a Planar Polynomial Differential System

本文研究一类形式相当一般的平面多项式系统赤道环量(Gauss球面的无穷远点奇点量)的计算,建立了系统赤道环量计算的简明的线性代数递推公式.应用递推公式计算赤道环量,只需用系统系数做四则运算,避免了通常计算赤道环量需要的复杂的积分运算和解方程,极易用计算机代数系统作符号推导并且不含舍入误差.

In this paper, we study the computation of quantities of equator （singular point quantities of infinity at Gauss sphere） in a class of planar polynomial differential system with a general form. Two linear recursion formulas for computation of quantities of equator are obtained. To compute quantities of equator with these recursion formulas, we only need to force addition, substraction, multiplication and division to the coefficients of the system, then avoid complex integrating operations and solving equations. It is symbolic and easy to realize without errors with computer algebra system.