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A polynomial in three variables is considered near a singular point where the polynomial itself and its partial derivatives vanish. A method for calculating asymptotic expansions in parameters for all branches of the set of roots of the polynomial near the singular point is proposed. The method is based on spatial power geometry and uses modern computer algebra algorithms: for calculating Gröbner bases and for work with algebraic curves. The implementation of the method is demonstrated on the example of a sixth degree poly nomial in three variables considered near infinity and near a degenerate singular point.

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