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Papers about Cadabra
The canonical introduction to Cadabra for high-energy physicists is the original paper (now updated for 2.x syntax),
hep-th/0701238 (now updated for 2.x syntax)
The Cadabra 2.x software is published as
Cadabra2: computer algebra for field theory revisited
A technical explanation of the motivation for writing this software, as well as a sketch of the internal structure, can be found in the paper
Please cite the three papers above when you use Cadabra in your own work; those citations are the only way to convince the bean counters that this software is useful!
A lot of information on the internals of Cadabra and various parts written by Dominic Price has appeared in his thesis,
Routines and Applications of Symbolic Algebra Software
The meld algorithm has also been documented in the paper
Hiding canonicalisation in tensor computer algebra
Finally, a general introduction to the old version of Cadabra for a wider public can be found in
A proper introduction to the new features of Cadabra 2 may appear at some point in the future.
Introductory papers to learn Cadabra
Leo Brewin has written a very thorough new introduction to Cadabra for people who intend to use it in General Relativity, with loads of examples suitable for beginners,
Using Cadabra for tensor computations in General Relativityavailable as arxiv:1912.08839
Also from his hand is a nice paper on how to do Riemann normal coordinate expansions with Cadabra, now updated to use Cadabra2 notation,
Riemann Normal Coordinate expansions using Cadabraavailable as arxiv:0903.2087v2
Research papers citing Cadabra
The list of papers citing cadabra is getting too long to maintain by hand, but Google Scholar does an excellent job at it. See the list of papers citing the Comp.Phys.Comm. paper, the list of papers citing the hep-th paper and the list of papers citing the Cadabra2 paper.