Spectral sequences for the reduction to normal forms

Abstract

Here is described a method for the reduction to normal forms, based on a spectral sequence, constructed from the filtration of the Koszul complex determined by the partial derivatives of the function under discussion. We do not use explicitly any properties of spectral sequences or of Koszul complexes, but prove directly everything that is necessary for the practical calculations. The correspondence between our constructions and the ordinary algebraic constructions is described in [18].