Introduction to Redberry: the computer algebra system designed for tensor manipulation

In this paper we introduce Redberry - an open source computer algebra system designed to manipulate with symbolic tensorial expressions. It implements basic computer algebra system routines as well as complex tools for real computations in physics. Redberry core provides common for majority of computer algebra systems tools for expressions manipulation, generalized on tensorial objects, as well as tensor-specific features: indices symmetries, LaTeX-style input, natural dummy indices handling, multiple index types etc. The high energy physics package includes tools for Feynman diagrams calculation: Dirac and SU(N) traces, Levi-Civita simplifications and tools for one-loop calculations in general field theory. In the present paper we give detailed description of Redberry functionality: from basic manipulations with tensors to real Feynman diagrams calculation, accompanied by many examples. We also introduce graph representation of a tensor - the basic underlying idea of the Redberry architecture, which clarifies a deep connection between symbolic tensor algebra and computational graph theory. Redberry is written in Java 7 and provides convenient Groovy-based user interface and extensive API for developers. The source code of Redberry is covered by more then 800 tests. Redberry is available from <a href="http://redberry.cc.">this http URL</a>