High Quality Content by WIKIPEDIA articles! In mathematics, and especially differential topology and singularity theory, the Eisenbud–Levine–Khimshiashvili signature formula gives a way of computing the Poincare-Hopf index of a real, analytic vector field at an algebraicially isolated singularity. It is named after David Eisenbud, Harold Levine, and George Khimshiashvili. Intuitively, the index of a vector field near a zero is the number of times the vector field wraps around the sphere. Because analytic vector fields have a rich algebraic structure, the techniques of commutative algebra can be brought to bear to compute their index. The signature formula expresses the index of an analytic vector field in terms of the signature of a certain quadratic form. Данное издание представляет собой компиляцию сведений, находящихся в свободном доступе в среде Интернет в целом, и в информационном сетевом ресурсе "Википедия" в частности. Собранная по частотным запросам указанной тематики, данная...

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