The Dynamic Dictionary of Mathematical Functions

Abstract

Mathematical tables have long been used by developers of computer algebra systems. Special functions are implemented in a system using formulas obtained in these tables for the computation of their derivatives, series or asymptotic expansions, numerical evaluation, simplification, integral transforms,... Recently, more and more powerful algorithms have been developed by the computer algebra community, so that nowadays, the flow can be reversed and mathematical tables can be generated automatically for large classes of functions. The gains are obvious: a full automation of the process that reduces the risk for typographical or other errors; more flexibility and extra interactivity for the readers, not only in the navigation, but also in the choice of the actual functions or formulas they need. Our team has started the development of a Dynamic Dictionary of Mathematical Functions focusing on solutions of linear differential equations (available at http://ddmf.msr-inria.inria.fr/). This development raises several interesting issues. Algorithmic ones obviously, but also more fundamental ones (what exactly is needed to define a function?), or practical ones (how should the interaction between computer algebra systems and dynamic mathematical content on the web be organized?). The talk will discuss these issues and present some of the choices that were made in our design.