Euclid, Tarski, and Engeler Encompassed

. The research presented in this paper is situated in the framework of constraint databases that was introduced by Kanellakis, Kuper, and Revesz in their seminal paper of 1990. In this area, databases and query languages are defined using real polynomial constraints. As a consequence of a classical result by Tarski, first-order queries in the constraint database model are effectively computable, and their result is within the constraint model. In practical applications, for reasons of efficiency, this model is implemented with only linear polynomial constraints. Here, we also have a closure property: linear queries evaluated on linear databases yield linear databases. The limitation to linear polynomial constraints has severe implications on the expressive power of the query language, however. Indeed, the constraint database model has its most important applications in the field of spatial databases and, with only linear polynomials, the data modeling capabilities are limited and queri..