Expression templates for truncated power series

The truncated power series technique (differential algebra or DA) is a powerful tool for non-linear map analysis of accelerators. The most natural language for numerical DA´s is C++, since it is object oriented and has operator overloading. Traditional C++, though, can be inefficient for scientific programming due to creation of many temporaries and extra loops in overloaded operators. The recent expression templates technique allows a user to combine the elegance of the object oriented approach with the speed of procedural languages. The way it was created, it is not directly applicable for DA. We created a set of classes whose structure will be suitable for implementing DA vectors and maps. Classes realizing the expression templates technique are separated from the client classes, which allows their reuse for different mathematical concepts. Speed tests on the KCC compiler showed that new C++ classes for DA have the same speed as hand-coded C