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Calculation of the Kronecker-Poincaré index of algebraic curves with respect to algebraic fields on the plane. (Russian) Zbl 0742.34006
Let $$P$$, $$Q$$, $$\phi$$ be polynomials with real coefficients. Let $$K=\{(x,y)\in\mathbb{R}^ 2,\;\phi(x,y)=0\}$$ be a Jordan curve such that on $$K$$ there is no singular point of the vector field $$(P(x,y),Q(x,y))$$. The interior of $$K$$ is defined by $$\phi<0$$ and $$(\partial\phi/\partial x)^ 2+(\partial\phi/\partial y)^ 2\neq 0$$ on $$K$$. The author gives a purely algebraic algorithm for calculation of the Kronecker-Poincaré index which uses a finite number of elementary algebraic operations of the coefficients of $$P$$, $$Q$$, $$\phi$$.

##### MSC:
 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.