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The ESF is an automatically generated encyclopedia of special functions: the entire mathematical material of the ESF is computed and typeset automatically without any human intervention. This extended abstract presents the mathematical background of the ESF.
The system MAD is a software package for authoring documents in Maple.
The K-sat problem features a phase transition between "easy to solve" and "hard to solve" as a parameter is varied. Phase transitions are observed in many physical systems as well. The Viana-Bray hamiltonian that describes spin glasses is thus reformulated in terms of the K-sat dialect. The Davis-Putnam algorithm is then used to investigate experimentally the structure of the ground state (lowest energy) configurations of spin glasses. This thesis was supervised by Olivier Martin and Rémi Monasson. Note: Vincent Puyhaubert adopts a combinatorial approach to the theoretical K-sat problem (formats ps, pdf).
I am a Maple lover and I have developped the following softwares.
|MAD (Mathematical Abstract Document) is a package for authoring documents with mathematical content directly from Maple and for exporting these documents into LaTeX, PostScript, PDF and HTML. Browse the documentation.|
I'm discovering the world of Special Functions. It is a tough job, since nobody knows exactly what a Special Function is! Indeed, a function is said to be special when it arises often in calculations: this is a somehow vague definition. In particular, there is no algebraic structure that contains all known Special Functions (a list may be found in the Handbook of Mathematical Functions, by M.Abramowitz and I.A.Stegun or in its on-line version and at Wolfram).
I focus on Special Functions that share the property of being solution of a linear differential equation with polynomial coefficients. These functions are called D-finite; about 60% of known Special Functions fall into the D-finite class. This class has been widely studied and a whole bunch of algorithms is applicable.
My supervisor came up with the exciting idea of using these algorithms, while extending them, in order to generate automatically the The Encyclopedia of Special Functions. I am developping this encyclopedia.
Ludovic Meunier, INRIA Rocquencourt, B. P. 105, F-78153 Le Chesnay Cedex (France)