Computing normalizing transformations

Given a singularity and a versal deformation of it, an arbitrary deformation can be induced from the versal one by a smooth transformation of coordinates and parameters. An algorithm was developed to compute this transformation, for deformations of functions. It requires a procedure to solve the infinitesimal stability equation, which is provided by the normal form map NFΨ related to a standard ideal basis (see Chap. 6). A similar approach works for the case of deformations of maps, involving left-right tangent spaces instead of ideals