Algorithms and computer algebra from particle physics

I report on two programs, “gTybalt” and “nestedsums”, which were originally developed for the calculation of quantum loop corrections in particle physics. However, these programs solve tasks, which are not specific to particle physics. The first one, “gTybalt”, is a free computer algebra system based entirely on open-source code. The program is build on top of other packages. It offers the possibility of interactive symbolic calculations within the C++ programming language. Mathematical formulae are visualized using TeX fonts. The second package, “nestedsums”, is a program library containing algorithms which allow the expansion of higher transcendental functions. These algorithms were developed by ourselves and used to solve otherwise unknown loop integrals. Applications of these algorithms extend to other branches of science, for example to number theory in mathematics.