The newgenesis C++ software package
Online computation of a Philip Hall Basis of a Free Lie Algebra
You said Rough Paths?
Synopsis.
This web page is dedicated to the project Digital Descriptions for Serial
Data Streams. I have started my work on this project as a post-doc at the
Mathematical Institute of Oxford
(2002-07 to 2003-07), under the advisory of
Pr. Terry J. Lyons and
Dr. Ben Hambly, using
funding provided by
MathFIT/EPSRC-LMS grant
GR/R2962/8/01 [HBKBU].
You can have a rough technical report
(dated
2004-02-25)
on my work at the Oxford Mathematical Institute
[DVI
69k,
PS
412k,
PDF
311k].
Keywords.
Rough Paths, Stochastic Analysis, Digital Description of Serial Data Streams,
Signal Processing, Inverse Problems,
Data Compression, Information Theory, Free (Lie) Algebras, Heisenberg Groups.
The newgenesis C++ software package consists in
The aim of newgenesis is to provide a software framework to test various ideas related to Rough Paths Theory for sound compression and digital description of serial data streams. The current development environment for newgenesis is GCC under Debian GNU/Linux.
The latest published version of newgenesis is 20050617. You can download an archive containing the C++ source code, the examples, and the documentation [tgz 1.2M]
You can have some rough documentation for newgenesis, produced with Doxygen.
newgenesis is developed by D. Chafaï (2002-now), partly under the advisory of T. J. Lyons (2002-2003). The library code of newgenesis is protected by the GNU Lesser General Public License, the programs code is protected by the GNU General Public License, whereas the documentation is protected by the GNU Free Documentation License.
Note. I believe that generic programming is the right way for mathematicians to do programming, since it corresponds to the conceptualisation aspects of data structures and algorithms regardless of the precise implementation in terms of data types. Generic programming is provided for example by C++ and ADA. Unfortunately, there is no Standard Templates Library (STL) equivalent for ADA to my knowledge. However, C++ is not perfect. Its ISO standard is sometimes obscure and the language itself is in the same time limited and too complex. Even if C++ is the de facto industry standard, it could be interesing to implement newgenesis in a smarter programming language.
This CGI program computes a Philip Hall basis of a free Lie algebra. It makes use of the libalgebra code provided by the newgenesis software package. Enter the requested numbers to get the Hall basis elements.
