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We obtain a parametric normal form for any non-degenerate perturbation of thegeneralized saddle-node case of Bogdanov--Takens singularity. Explicit formulasare derived and greatly simplified for an efficient implementation in anycomputer algebra system. A Maple program is prepared for an automaticparametric normal form computation. A section is devoted to present somepractical formulas which avoid technical details of the paper.

Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case