Package for Calculations and Simplifications of Expressions with Dirac Matrixes (MatrixExp)

Abstract

This paper describes a package for calculations of expressions with Dirac matrixes. Advantages to existing similar packages are described. MatrixExp package is intended for simplification of complex expressions involving $\gamma$-matrixes, providing such tools as automatic Feynman parameterization, integration in $d$-dimensional space, sorting and grouping of results in a given order. Also, in comparison with existing similar package Tracer, presented package MatrixExp has more enhanced input possibility. User-available functions of MatrixExp package are described in detail. Also an example of calculation of Feynman diagram for process $b\to s\gamma g$ with application of functions of MatrixExp package is presented.