The Dynamic Dictionary of Mathematical Functions (or DDMF, http://ddmf.msr-inria.inria.fr/) is an interactive website on special functions inspired by reference books such as the NIST Handbook of Special Functions. The originality of the DDMF is that each of its “chapters” is automatically generated from a short mathematical description of the corresponding function.
To make this possible, the DDMF focuses on so-called D-finite (or holonomic) functions, i.e., complex analytic solutions of linear ODEs with polynomial coefficients. D-finite functions include in particular most standard elementary functions (exp, log, sin, sinh, arctan...) as well as many of the classical special functions of mathematical physics (Airy functions, Bessel functions, hypergeometric functions...). A function of this class can be represented by a finite amount of data (a differential equation along with sufficiently many initial values),
and this representation makes it possible to develop a computer algebra framework that deals with the whole class in a unified way, instead of ad hoc algorithms and code for each particular function. The DDMF attempts to put this idea into practice.
In this talk, I will present the DDMF, some of the algorithms and software libraries behind it, and ongoing projects based on similar ideas, with an emphasis on symbolic-numeric algorithms.
- Computational Mathematics and Applications Seminar