This paper makes a contribution to differential elimination and more precisely to the problem of computing a representation of the radical differential ideal generated by a system of differential equations (ordinary or partial). The approach we use here involves characteristic set techniques;‡ these were introduced by J. F. Ritt, the founder of differential algebra. The basic idea is to write t...

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In the paper the ideas of relative Nevanlinna L∗-order and relative Nevanlinna L∗-lower order of an analytic function with respect to an entire function in the unit disc U = {z : |z| < 1} are introduced. Hence, we study some comparative growth properties of composition of two analytic functions in the unit disc U on the basis of relative Nevanlinna L∗-order and relative Nevanlinna L∗-lower order.

We shall prove the following analogue of a theorem of Kronecker's : Let J be a difference field containing an element t which is distinct from its transforms of any order. Every perfect ideal in the ring 7\yu ' ' ' y y<n\ has a basis consisting of n + 1 difference polynomials. The corresponding theorem for differential polynomials was proved by J. F. Ritt. We shall follow in all but details a b...