CDIFF: a REDUCE package for computations in geometry of differential equations
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About CDIFF
The name 'CDIFF' comes from the fact that the package allows to do computations with differential operators in total derivatives, i.e. C-differential operators, for differential equations in even and odd variables.
The package was developed in the early '90s at the University of Twente by the following researchers:
- Peter Gragert
- Paul Kersten
- Gerhard Post
- Marcel Roelofs
The 'Twente' part of CDIFF has been recently included in the official REDUCE distribution on sourceforge. It can run on Linux and Windows, both 32-bit and 64-bit, as well as Mac OS.
Recently, Raffaele Vitolo wrote new code about automatic generation of differential consequences and of ansatz for solving determining equations of symmetries. The code and a user guide is available at this website (see below).
System requirements
In the University of Twente Paul Kersten uses the package under the Linux version of PSL REDUCE 3.7.
Tests done by Raffaele Vitolo shows that packages works smoothly under the Linux version of PSL REDUCE 3.8 and under the modern open source CSL version for Linux (32bit and 64bit) and Windows. A 64bit operating system with a CSL version is suggested in order to be able to use more memory. The most recent computations are performed with 64-bit Linux and the most recent binary build of the CSL version from Sourceforge.
For PSL REDUCE every session should be started with
lisp set_bndstk_size 1000000;
Twente CDIFF package: documentation, user guide and examples
The 'Twente' part of CDIFF package (including documentation, user guide and examples) is included in the official Reduce distribution, but can be downloaded here:
- Supervf.red - The Super vectorfield package for REDUCE 3.4, Revision: 1.1
- Integrator.red1 - The Integrator package for REDUCE 3.4, Revision: 1.0
- Tools21.red - The Algebraic operator tools for REDUCE 3.6, Version 2.1 (August 14, 1996)
- TwenteReduceAdd.zip - Auxiliary source files
The following papers describe the REDUCE functions, written in REDUCE symbolic mode (which is based on Standard Lisp), which are provided by the Twente CDIFF packages.
Raffaele Vitolo wrote a user guide to Twente CDIFF packages. It explains:
- how to install and use REDUCE+CDIFF in Linux and in Windows;
- how to write CDIFF programs for various types of computations like: higher symmetries and conservation laws, local and nonlocal Hamiltonian operators, etc.
Examples discussed in the user guide are also available. In the user guide examples of computations are performed for evolutionary PDEs.
New software in CDIFF package: user guide and examples
Raffaele Vitolo wrote new software in CDIFF package (latest version: 28/01/2012). It is devoted to computations for general differential equations (i.e., not necessarily in evolution form) with an arbitrary number of independent variables. It can compute symmetries, conservation laws, Hamiltonian, symplectic and recursion operators, in local and nonlocal coordinates. It is distributed under the same free license of REDUCE.
The above zip file contains:
- A README.txt file;
- The program file cde.red, for computations of differential consequences of even and odd partial differential equations and of the related total derivatives.
- The program file cdj.red, for computations with total derivatives on jet spaces.
- The file Cdiff-userguide-2.pdf, a CDIFF user guide for computations of symmetries, conservation laws, Hamiltonian, symplectic and recursion operators, in local and nonlocal coordinates.
- The file global.txt with a list of global variables used in cde.red.
- The folder examples, which contains all examples described in the user guide with results and debug files.
Note that the last version is still not covered by the documentation; this will be fixed as soon as possible.
The author welcomes comments and questions on CDIFF.
