Parametric Expansions of an Algebraic Variety near Its Singularities

Presently, there is a method based on Power Geometry that allows one to find asymptotic forms and expansions of solutions different kinds non-linear equations near their singularities. The contains three algorithms: (1) Reducing the equation its normal form, (2) separating truncated equations, (3) power transformations coordinates. Here, we describe for simplest case, single algebraic equation, apply it an variety, as described by order 12 in variables. variety was considered study Einstein’s metrics has several singular points curves. Near some them, compute local parametric expansion variety.