Department of Mathematics Tennessee Technological University

(Released: November 18, 1998)
(Last Revised: April 21, 2003)

CLIFFORD - A Maple 6 Package for Clifford Algebra Computations
(version 6, December 27, 2002)
with Cliplus, Bigebra, Define, GTP, and Octonion

Rafal Ablamowicz (*) and Bertfried Fauser (**)

(*) Department of Mathematics, Box 5054
Tennessee Technological University, Cookeville, TN 38505
phone: USA (931) 372-3569, fax: USA (931) 372-6353
 rablamowicz@tntech.edu

Files listed below contain version 6 of the package CLIFFORD for Clifford algebra computations in Maple 6 along with supplementary packages described below::

• CLIFFORD - for computations in Clifford algebras Cl(V,B) where dim V <=9, and B is an arbitrary bilinear form in V
• Bigebra - for computations with Hopf gebras and bi-gebras
• Cliplus - extends CLIFFORD to other bases such as the Clifford basis or the dotted wedge basis.
• Define - fixes Maple's 'define'
• GTP - extends CLIFFORD to graded tensor products of Clifford algebras.
• Octonion - for computations with octonions and octonionic matrices.

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DISCLAIMER: THERE IS NO WARRANTY FOR THE CLIFFORD, Bigebra, Cliplus, Define, GTP, and Octonion PACKAGES TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANT ABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
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You can find out how I use CLIFFORD by going to my recent publications page.

HIGHLIGHTS OF NEW FEATURES IN VERSION 6:

• This is a direct translation of CLIFFORD ver. 5 from Maple V Rel. 5.1 to Maple 6. The table-based code from Maple V has been converted to module-based programming language of Maple 6.
• There are a few additional procedures in CLIFFORD and Bigebra while Define is a new patch for Maple's define function.
• To install all needed libraries, download libraries.
• To see all features, open help pages in Maple 6 (see below how) that are already included in the library files, or download documentation in .pdf format for printing and/or viewing in Adobe Reader.
• To see the Maple code of each module, download codes.
• To view installation instructions, go to section on installation under Windows, Linux, or download README.txt.
• To see how to test your installation go to section on testing installation.

INSTALLATION INSTRUCTIONS:

A. For Windows:

• Make sure you run Maple 6 (or any of its updates, for example, Maple 6.02).
• Download library_M6.zip . Just right click on the link and then save to your system to some temporary directory and unzip it there. It contains four files: maple.hdb, maple.lib, maple.ini, and maple.ind.
• Create a directory where you will store all library files. Default directory name used in maple.ini file is \Cliffordlib in the directory C:\Maple6. To use the default, create first a directory \Maple6 on C:\ drive and then a subdirectory \Cliffordlib in the directory C:\Maple6.
• Copy files maple.hdb, maple.lib, and maple.ind to C:\Maple6\Cliffordlib.
• Copy maple.ini to \BIN.WNT or \Users subdirectory of your Maple 6 directory.
• If you want to install CLIFFORD and its supplementary packages in a directory other than C:\Maple6\Cliffordlib, you may do so but you will need to modify accordingly the single line in maple.ini. Make sure you type the path correctly and appropriately for your operating system.
• Test that installation has been done correctly (see below)

B. For Linux (if you have access to the root directory):

• 1. Download library_M6.zip from http://math.tntech.edu/rafal/cliff6/ (just right click on the link and then save to your system).
• 2. Change to root:

> su

• 3. Create a library directory in the maple path: Maple may be installed in /usr/local/maple called $MAPLE_PATH in the following

> mkdir $MAPLE_PATH/Cliffordlib

• 4. Copy the zip-file into this dir and unzip:

> cp library_M6.zip $MAPLE_PATH/Cliffordlib
> cd $MAPLE_PATH/Cliffordlib
> unzip library_M6.zip
Then proceed with 5a) if you have only maple6 running and with 5b) if you  have several maple versions running

• 5a. Change the .mapleinit file to accept the library as *first* entry in 'libname':

> exit              (* close root shell *)
> cd                (* go to home dir *)
> pico .mapleinit   (* pico / or vi editors *)
Add the line:
libname:=`$MAPLE_PATH`,libname;
and store the file (create it if necessary) as .mapleinit.
The initialization is finished. If you have any problems with installation under Linux, please contact Dr. Bertfried Fauser at: Bertfried.Fauser@uni-konstanz.de   or  fauser@spock.physik.uni-konstanz.de.

• 5b. Stay being root!

> cd ../bin
open the file maple, and look for the place where xmaple6 is called change this line to (no white space after \ or type a single line only
> exec ${MAPLE}/$MAPLE_SYS_BIN/xmaple6 -km p -b ${MAPLE}/Cliffordlib \ -b ${MAPLE}/lib $INCLUDES $PARAM and change the line where mapleTTY is loaded to
>  exec ${MAPLE}/$MAPLE_SYS_BIN/mapleTTY -b ${MAPLE}/Cliffordlib \ -b ${MAPLE}/lib $INCLUDES $PARAM
(The option -b makes maple aware of locations of libraries. In this way you might want to change every start script of several maple versions to find their own local libraries, e.g., Maple V using Cliff5  /BIGEBRA /Cli5plus /Octonion /GTP or others)
> exit
leave root shell.

C. For Linux (if you do not have root access):

• 1. Download library_M6.zip from http://math.tntech.edu/rafal/cliff6/ (just right click on the link and then save to your system).
• 2. Create a library directory in your home directory (* if you choose  a name starting with a dot, this dir is not displayed by default *)

> cd           (* go to home dir *)
> mkdir .Cliffordlib

• 3. Copy the zip-file into this dir and unzip:

> cp library_M6.zip ./.Cliffordlib
> cd .Cliffordlib
> unzip library_M6.zip

• 4. Change the .mapleinit file to accept the library as *first* entry in the variable 'libname'

> cd                  (* go to home dir *)
> pico .mapleinit     (* pico / or vi editors *)

• 5. Ad the line:

libname:=`<homedirectory>/.Cliffordlib',libname;
and store the file (create it if necessary) as .mapleinit.

• 6. The initialization is finished.
• 7. Unfortunately there is only one .mapleinit file for every maple version. This means that other versions of maple will use this directory too,

which might cause PROBLEMS. Currently there is no workaround for this and we recommend to insert the line
libname:=`<homedirectory>/.Cliffordlib',libname;
in the first line of any worksheet which use Clifford/Bigebra for maple6
Such a maple file looks like:
> restart: libname:=`<homedirectory>/.Cliffordlib',libname;
> with(Clifford):with(Bigebra): ## optional:  with(Cliplus):with(Octonion):with(GTP):
In this case no library path is needed. If you run several versions of  maple you might contact your local administrator 'root' to change the startup scripts as described above.

• Start Maple 6.
• To load the main module, at the Maple prompt, type:

>with(Clifford);

When the package is loaded, you should see a list with names of available procedures. If the package has not loaded and you get an error message make sure that files maple.hdb, maple.lib, and maple.ind extracted from library_M6.zip are all located in the directory such as C:\Maple6\Cliffordlib and that the path to that directory is included in maple.ini file. To see if maple.ini has been executed, type
>libname;
and Maple should respond with

            "C:\\Maple6/Cliffordlib", "C:\\Maple6/lib"

if maple.ini had this line:

libname:="C:\\Maple6/Cliffordlib",libname:
 

• To load other packages, issue with(packagename); command as well, where 'packagename' is one of Bigebra, Cliplus, GTP, or Octonion.
• To check if help pages are available in the browser, at the Maple prompt type:

>?Clifford
You should then see the introductory page for CLIFFORD and at the top of the screen you should see Maple browser opening four vertical windows with words Clifford and intro highlighted in the two rightmost panels. You should also see, above and below Clifford, names of other packages for which help should now be available.
• To navigate through the help pages, begin with the introductory help page for CLIFFORD as described above and follow links within. You can also issue this command at the Maple prompt:

>?Clifford,intro

More information about the use of this package as well as the use of other software packages written in Mathematica, Reduce, Matlab, C++, Fortran, Clical, and Maple for the Clifford algebra research, see the following book and associated with it electronic files located at the Birkhauser Web site:
www.birkhauser.com/book/ISBN/0-8176-3907-1/

Title: ``Clifford Algebras with Numeric and Symbolic Computations''
Editors: Rafa\l Ab\lamowicz, Pertti Lounesto, Josep M. Parra
ISBN: 0-8176-3907-1
Birkhauser, Boston
Year: 1996

For more on Clifford algebras and their applications see also:

Title: ``Clifford Algebras and their Applications in Mathematical Physics - Vol. 1 Algebra and Physics, Vol. 2 Clifford Analysis''
Editors: Rafal Ablamowicz and Bertfried Fauser (Vol. 1),  John Ryan and Wolfgang Sproessig (Vol. 2)
ISBN: 0-8176-4182-3 (Vol. 1), 0-8176-4183-1 (Vol. 2) [for more information go to http://math.tntech.edu/rafal/mexico/mexico.html]
Birkhauser, Boston
Year: 2000

Title: ``Clifford Algebras and Spinor Structures -- A Special Volume Dedicated to the Memory of
Albert Crumeyrolle (1919 -- 1992)''.
Editors: Rafal Ablamowicz, Pertti Lounesto
ISBN: 0-7923-3366-7
Kluwer, Dordrecht
Year: 1995

Please direct all questions, comments, and reports on bugs to:

Rafal Ablamowicz rablamowicz@tntech.edu
Department of Mathematics, Box 5054
Tennessee Technological University
Cookeville, TN 38505
phone: USA (931) 372-3569
fax: USA (931) 372-6353

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Last updated: April 21, 2003/ra