Using the Euler–Jacobi formula we obtain an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar cubic polynomial differential systems when these systems have nine finite singular points.

中文翻译：

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平面三次多项式系统的奇异性与Euler Jacobi公式

使用Euler-Jacobi公式，我们可以得出多项式矢量场的奇异点与其拓扑指数之间的代数关系。使用此公式，当平面三次多项式微分系统具有9个有限奇异点时，我们可以获得奇异点的配置及其拓扑指数。