Frédéric Chyzak (INRIA Rocquencourt, France)

A DynaMoW for the presentation of dynamic mathematics on the web (Thursday 14h15–15h). We report on the design and implementation of a programming tool, DynaMoW, to control interactive and incremental mathematical calculations to be presented on the web. This tool is implemented as a language extension of OCaml using Camlp4. Fragments of mathematical code written for a computer-algebra system as well as fragments of mathematical web documents are embedded directly and naturally inside OCaml code. A DynaMoW-based application is made of independent web services, whose parameter types are checked by the OCaml extension. The approach is illustrated by two implementations of online mathematical encyclopedias on top of DynaMoW.

This is joint work with Alexis Darrasse.

Gabriel Dos Reis (Texas A&M University, USA)

On programming language geared toward computational mathematics (Friday 9h30–10h15).

Joris van der Hoeven (CNRS & École polytechnique, France)

Advanced use and new features of TeXmacs (Thursday 10h45–11h30). In this follow-up presentation of the talk by Francois Poulain, we will demonstrate some of the more advanced features of TeXmacs, such as the creation of graphics, tables and presentations. We will also show different ways to use TeXmacs as an interface to computer algebra sessions: traditional shell-like interfaces, using the CAS in the background, and a recent new feature: spreadsheets.

Joris van der Hoeven (CNRS & École polytechnique, France)

The Mathemagix language (Friday, 10h45–11h30). General purpose systems for computer algebra such as Maple and Mathematica incorporate a wide variety of algorithms in different areas and come with simple interpreted languages for users who want to implement their own algorithms. However, interpreted languages are insufficient in order to achieve high performance, especially in the case of numeric or symbolic-numeric algorithms. Also, the languages of the Maple and Mathematics systems are only weakly typed, which makes it difficult to implement mathematically complex algorithms in a robust way.

Since one major objective of the Mathemagix system is to implement reliable numeric algorithms, a high level compiled language is a prerequisite. The design of the Mathemagix compiler has been inspired by the high level programming style from the Axiom and Aldor systems, as well as the encapsulation of low level features by languages such as C++. Moreover, the compiler has been developed in such a way that it is easy to take advantage of existing C++ template libraries. In our presentation, we will give an overview of what has been implemented so far and some of the future plans.

Grégoire Lecerf (CNRS & École polytechnique, France)

The C++ libraries of Mathemagix (Thursday, 15h00–15h45). We will present the implementations of the elementary operations with polynomials and matrices available in the C++ libraries of Mathemagix. This includes most of the classical methods for univariate polynomials and series, but also very recent techniques with several variables. Dedicated variants have been designed for numerical types. We will illustrate some of the possibilities offered for certified numeric computations with balls and intervals. Most of the algorithms can benefit from parallelization and vectorization features.

This work is in collaboration with J. van der Hoeven.

Bernard Mourrain (INRIA Méditerranée, France)

Geometric Modeling and Computing with Mathemagix (Thursday, 16h15–17h00). Geometric Modeling requires dedicated tools for manipulation, computation and vizualisation of geometric objects. We will present the algebraic-geometric modeler AXEL and its integration in the Mathemagix project. This tool allows to visualize and compute with different types of tridimensional models of shapes. The main representations include point sets, meshes, rational, bspline, algebraic and semi-algebraic curves and surfaces. It is also a platform which integrates geometric algorithms, through an open mechanisms of plugins. We will describe its design, its extension mechanism, its main plugins, some of the algorithms involved in the computation with semi-algebraic sets or bsplines.

François Poulain (ANR/CNRS & École polytechnique, France)

Introducing TeXmacs to new users (Thursday, 9h30–10h15). GNU TeXmacs is a free software for structured editing with special features for scientists. It aims to provide a unified and user friendly framework for editing documents with different types of content (text, mathematics, graphics, interactive content, etc.). For this purpose, TeXmacs includes a text editor with support for mathematical formulas, a small figure editor, and also numerous features like a presentation mode, an orthographic correction, a revision control system, etc. Moreover, TeXmacs can be used as an interface for many external systems for computer algebra (Mathemagix, Maxima, etc.), numerical computation (GNU Octave, Scilab), statistics (GNU R), etc.

In this presentation, we will firstly take a tour of the basics needed to quietly tackle TeXmacs (structured edition and ergonomic principles). Then, we will illustrate some features through the writing of a scientific article. Finally, we will demonstrate some use cases needing interoperability with LaTeX, on which a strong effort is currently put.