New methods for building computer algebra systems

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The main objective of this research is to fundamentally re-examine the methodology currently used to build Computer Algebra Systems, aiming to make substantial improvements. Computer Algebra Systems (CAS) are well-known to be at the forefront of many new programming language technologies (generic programming, dependent types, first-class types, etc), as well adopting advanced software engineering techniques long before they are popular in the mainstream. While the development of new, faster algorithms in the area of Computer Algebra has proceeded at a breakneck pace in the last few years, engineering issues have received less attention. However, recent progress in such areas as type theory, denotational semantics for nominal languages, generative programming and automated testing can all be profitably applied to the construction of CASes.