Algolib: The Algorithms Project’s Library and Other Packages of the Algorithms Project. Combinatorial analysis, discrete mathematics and computer algebra are the main interests of the Algorithms Project. Our packages let you specify, generate, and enumerate combinatorial structures; manipulate the associated generating functions, functional equations or recurrences; study their asymptotic behaviour. The interplay between these applications serves the Algorithms Project’s main goal of the automatic complexity analysis of algorithms. However, long-term research in this direction has induced the development of other packages for the manipulation of linear differential and difference operators, Groebner basis calculations, and the symbolic summation and integration of special functions and combinatorial sequences. Special emanations of the above are the Algolib library, which collects most of our programs in a single archive, and the encyclopedia of combinatorial structures, which allows access by keywords, combinatorial specifications, generating function, closed-form or by the first integers in the enumeration sequence to many combinatorial structures. A lot of it was automatically generated using combstruct, gfun, and gdev. Studies in Automatic Combinatorics are extensive example sessions that serve as an introduction to the use of our packages, together with advanced sessions illustrating their use in the study of combinatorics, special functions or asymptotic analysis. Also available as Maple help pages in the Algolib library.

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