Cadabra

Cadabra is a computer algebra system designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many more. The input format is a subset of TeX. Both a command-line and a graphical interface are available.

Key features of Cadabra:

• Input and output using TeX notation.
• Designed for field-theory problems, with handling of anti-commuting and non-commuting objects without special notations for their products, gamma matrix algebra, Fierz identities, Dirac conjugation, vielbeine, flat and curved, covariant and contravariant indices, implicit dependence of tensors on coordinates, partial and covariant derivatives...
• Powerful tensor simplification algorithms, not just for mono-term symmetries but also for multi-terms symmetries like the Bianchi identity, or dimensionally-dependent symmetries like the Schouten identity.

Technical highlights:

• A multiple-inheritance typing system using properties.
• Open source C++ code, with documentation on how to extend the system with new algorithm modules.

 2007–2009 Alexey Beshenov.
Contact: al@cadadr.org.