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Power geometry and algebraic equations

A. SoleevSamarkand State University, Samarkand 703004, UzbekistanN. SoleevaSamarkand State University, Samarkand 703004, Uzbekistan
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We consider a polynomial depending on three variables near its singular point where the polynomial vanishes with all its first partial derivatives. We propose a method of computation of asymptotic expansions for all branches of the set of roots of the polynomial near the mentioned singular point. The method of computation is based on the space Power Geometry [2].

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