Piecewise algebraic functions

Abstract

This paper contains a thorough study of piecewise algebraic sets and functions. They are built up using finitely many parts, each of which is defined by finitely many algebraic equations or inequalities. They occur naturally in many concrete situations which are demonstrated by applications in linear algebra, complexity theory, and meromorphic differential equations. We also emphasize that in many cases effective procedures are given for the calculation of the various objects.