For the successful evolution of Magma it is important that we have a detailed knowledge as to where and how it is applied. As one approach to obtaining such information we have undertaken a fairly unsophisticated search of the web for publications that refer to Magma or Cayley (the predecessor of Magma), either in the bibliography or in the text proper. Our database is by no means exhaustive, and we continue to discover items not in our collection.
Approximately 3000 citations have been found: roughly 200 refer to Cayley, and the remainder to Magma. In the lists published here we have included books, papers, PhD theses, preprints posted to the arXiv (unless they are published), and a small collection of other publications that are of special interest. Some 200 items referring to Magma have been omitted; these comprise of:
This culling procedure is not complete as there are many items where we have lacked either time or access to the text.
One feature of the database is the classification of the items into categories based substantially on MSC codes; this helps identify those areas of mathematics in which Magma finds a significant number of applications. We plan to do a more detailed analysis on a selection of the papers in order to gain a deeper understanding of the role Magma plays.
The database can be viewed online here. A list of the 100 authors who appear most frequently in the database can be found here.
We welcome corrections and additions – if you have an appropriate publication not included in the current list, please email us the publication details. If you use Magma in a non-trivial way in your research then we strongly encourage you to mention this in the text and also to include a citation in your bibliography.
An initial search by Michael Gleeson in early 2006 located approximately 1000 papers. In early 2007, Paul Tiffen identified a further 900 papers and this was the basis of the 2007 edition of this bibliography. Paul Tiffen collected a further 700 papers in 2008 and early 2009 while Michael Gleeson added a further 400 papers in September 2009. A pruned version of these lists formed the basis of the 2009 edition.
The papers on coding theory up to 2006 were collected by Greg White. Amongst others, Philippe Cara, Marston Conder, Markus Grassl, Masaaki Harada, George Havas, Jenny Key, Dimitri Leemans, Eamonn O'Brien, and Martin Rötteler were kind enough to provide us with lists of their publications relating to Cayley and Magma.
We acknowledge the debt we owe to the Mathematical Reviews database which greatly facilitated this exercise.