Maylis Delest
University of Bordeaux I, France.
Email: maylis@labri.u-bordeaux.fr
Jean-Marc Fédou
University of Nice, France.
Email: fedou@diamant.unice.fr
Mathematics and Computer Science books have always contained many figures whose unique defect is that they only reflect a particular case. The reader has then to create its own examples and this even in the most complex cases. The generic example imagined by the editor of the book is in the most usual and does not reflect the extreme phenomena. With the multimedia tools, a thinking mode is born at publishers to propose interactive books. The interactive version on the network has to allow the user to choose its own examples and to see how they run on the quicksort algorithm without loading or owning any programs.
We propose to use the CalICo environment to realize such books for some fields related to discrete objects in Mathematics or Computer Science. CalICo was developed for drawing easily discrete objects in Combinatorics from their usual coding driving interfaces from computer algebra softwares. Combinatorics has always been concerned by images and drawings because they give interpretations of enumeration formulae leading to simple proofs of these formulae, and sometimes they are themselves central to the problem. Some libraries or programs already exists that performs such actions. For example, we can quote the Mathematica library done by Skiena ([Ski90]) which give tools for implementing graphs objects. This library does not allow to have interaction with the graphics itself.
The CalICo environment offers a communication tool which allows interactions with Maple, CAML and graphical interfaces for trees, graphs, permutations, paths, polyominoes. It gives also some library in order to connect others interpretors or a C-program. Thus the main quality of this environment is that it allows the user to program the pictures and thus the animations through his favorite language. A complete description can be found in [Rou94] and [DFMR97].
In this talk, we will show how the user can
Bibliography
[Bro92] M. Brown.
Algorithm animation : techniques, a system and a novel application.
Workshop on Computational Support for Discrete Mathematics, Rutgers
Center University, 1992.
[DFMR97] M. Delest, J.M. Fédou, G. Melançon, and N. Rouillon.
Computation and images in combinatorics.
In RIACA Amsterdam, editor, HISC book Springer Verlag, to be published in 1997.
[Rou94] N. Rouillon.
Calcul et Image en Combinatoire.
PhD thesis, Université Bordeaux I, December 1994.
[Ski90] S. Skiena.
Implementing discrete Mathematics : Combinatorics and graph
theory with Mathematica.
Addison-Wesley, 1990.
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