POWER GEOMETRY IN LOCAL RESOLUTION OF SINGULARITIES OF AN ALGEBRAIC CURVE
The main goal of this work is to provide a consistent set of general-purpose algorithms for analyzing singularities applicable to all types of equations. We present the main ideas and algorithms of power geometry and give an overview of some of its applications. We also present a procedure that allows us to distinguish all branches of a spatial curve near a singular point and calculate the parametric appearance of these branches with any degree of accuracy. For a specific case, we show how this algorithm works.
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