sumit

Σ it -- an ALDOR library for linear differential and difference equations. We describe how the computer algebra library Σ it has evolved from a special-purpose embeddable library to a general purpose ALDOR computer algebra library with special emphasis on efficient algorithms for solving linear ordinary differential and (q)-difference equations. After a short tour of the algorithms recently implemented in Σ it , we outline in particular its following design aspects: Its use of advanced features of the ALDOR programming language (postfacto extensions and callbacks) to combine abstract data types and generic algorithms with efficient special algorithms for specific types. Its implementations of the algorithms of differential Galois theory over non-algebraically closed constant fields, allowing for efficient future generalisations to linear partial differential equations. Its use of abstract generic parsers and interpreters to allow easy communications between Σ it clients and interactive programs (e.g. MAPLE, graphical user interfaces, web services, etc).