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We present some of the experiments we have performed to best test our design for a library for MathScheme, the mechanized mathematics software system we are building. We wish for our library design to use and reflect, as much as possible, the mathematical structure present in the objects which populate the library.
We describe in this paper new design techniques used in the cpp exact linear algebra library linbox, intended to make the library safer and easier to use, while keeping it generic and efficient. First, we review the new simplified structure for conta
Exascale computing will feature novel and potentially disruptive hardware architectures. Exploiting these to their full potential is non-trivial. Numerical modelling frameworks involving finite difference methods are currently limited by the static n
Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be trusted to write good code. In this manuscript we describe ModelingTo
The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to find such
We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algorithms can be implemented in Julia, without the need to resort to a low-