Multiplicity of the solutions of a differential polynomial
Two notions of multiplicity for the solutions (Puiseux series) of differential polynomials are proposed. The first one is based on the Newton-Puiseux-Fine polygon, and it is of a combinatorial nature. The second one is of a differential nature and extends the standard notion of algebraic multiplicity. It is shown that both concepts, defined independently, are equivalent. The limit of the multiplicity for a given differential polynomial is also established, and a precise procedure to reduce the multiplicity is given. Finally, the problem of computability of these entries, which still remains open, is presented.
multiplicity for solutions of differential polynomials
scientific article; zbMATH DE number 897487