Multivariable dimension polynomials and new invariants of differential field extensions (Q5957213)

The author investigates a special type of reduction in a ring of differential polynomials over a differential field of characteristic \(0\) whose basic set of operators is presented as a disjoint union of its subsets. Using the idea of Gröbner bases he develops the appropriate technique of characteristic sets that allows him to give a method of computation of multivariable dimension polynomials associated with a finitely generated differential field extension. The main result of the paper is a generalization of the classical ideas of E. R. Kolchin on differential birational invariants.