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An algorithm to compute the equations of tangent cones. (English) Zbl 0568.68029
Computer algebra, EUROCAM ’82, Conf. Marseille/France 1982, Lect. Notes Comput. Sci. 144, 158-165 (1982).
[For the entire collection see Zbl 0533.00024.]
An algorithm is presented which computes the defining equations of a tangent cone to an algebraic variety in its singular point. The equations are obtained in the form suitable for writing out the Gröbner base [B. Buchberger, Lect. Notes Comput. Sci. 72, 3-21 (1979; Zbl 0417.68029)] for the cone. A theoretical investigation of correctness and termination property of the algorithm is also performed. The implementation of the algorithm would facilitate mathematical experiments with tangent cones in the field of singularity classification.
Reviewer: A.Bocharev

68W30 Symbolic computation and algebraic computation
14B05 Singularities in algebraic geometry
32S05 Local complex singularities