This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively, in the context of (locally) essential domains.

This paper describes a probabilistic method for verifying the equivalence of two multiple-valued functions. Each function is hashed to an integer code by transforming it to a integer-valued polynomial and the equivalence of two polynomials is checked probabilistically. The hash codes for two equivalent functions are always the same. Thus, the equivalence of two functions can be verified with a ...

In this expository lecture, we explain how problems of classical polynomial algebra may be understood and numerically solved when they appear in the context of Scientific Computing, i.e. with data of limited accuracy. A suitable conceptual framework is introduced and its use explained in a number of situations.