CLIFFORD - A Maple 2017 Package for Clifford Algebra
Computations

Version 2017.1, September 4, 2017

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

(*) Department of Mathematics, Box 5054

Tennessee Technological University, Cookeville, TN 38505

phone: USA (931) 372-3622(931) 372-3622, fax: USA (931) 372-6353(931) 372-6353

rablamowicz@tntech.edu

(**) Universitat Konstanz, Fachbereich Physik,
Fach M678

78457 Konstanz, Germany

Bertfried.Fauser@uni-konstanz.de

bertfried.fauser@googlemail.com

Version 2017.1 of **CLIFFORD** for Clifford algebra computations in Maple 17 contains the following packages:

**CLIFFORD**- the main package for computations in Clifford algebras Cl(V,B) of an arbitrary bilinear form B**eClifford**- a new small and fast package for computations in Clifford algebras Cl(p,q,r) over vector space V of arbitrary dimension dim V = n = p+q+r which uses a new way to represent basis monomials as indexed names. The quadratic form Q in V may be degenerate and it has signature (p,q,r) with a possible degeneracy in r dimensions or none. A modified code to multiply two basis monomials uses Walsh functions. For more information see:**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**Octonion**- for computations with octonions and octonionic matrices**GfG**- experimental package for Groebner bases in Grassmann algebras**GTP**- extends**CLIFFORD**to graded tensor products of Clifford algebras**RJgrobner**- small package (with Jane Liu) for commutative Groebner bases. It does not need CLIFFORD/Bigebra.**SchurFkt**- package for the Hopf Algebra of Symmetric Function**SymGroupAlgebra**- an experimental package for computations in the group algebra of the symmetric group S_n**SP**- small package for symmetric functions. It does not need CLIFFORD/Bigebra.**Walsh package**- this package is included as a Maple worksheet, type [>?cmulWalsh3; at the Maple prompt.

**code_support**- a package to modify, copy, and insert help worksheets into Maple database. It does not need CLIFFORD/Bigebra.

**AVAILABLE FILES:**

- Download library_M2017.zip - A .zip file with all library files containing compiled code for
**CLIFFORD ver. 2017.1**including all help pages. [updated 09/04/2017] - For new installation instructions see README.txt. [updated 09/04/2017]
- Download Code_of_all_packages_for_Clifford_M17.zip - A .zip file with Maple code of all packages included in
**CLIFFORD ver. 2017.1**. [updated 09/04/2017] - A Maple tutorial for CLIFFORD ver. 16.1 from AGACSE 2012 (one .mws and one .mw worksheet): Tutorial_AGACSE2012.zip
- A Maple tutorial for CLIFFORD ver. 17.1 for Alterman Summer School, Brasov, Romania, August 1-9, 2016 (one .mw worksheet): Tutorial_Brasov_2016_M17.zip
- A Maple tutorial for CLIFFORD ver. 2017.1 for Alterman Summer School, Sofia, Bulgaria, July 31-August 4, 2017 (one .mw worksheet): Tutorial_Sofia_2017_M2017.zip

You can find out how I use **CLIFFORD** by going to my recent publications page.

- maple.ini file has been modified due to a different way Maple 2017 reads and saves files, that is, an explicit complete path to a directory where an .m file is located must be included in the 'read' statement. Thus, it is convenient to store such files in the same directory as the one saved in 'savelibname'. For example, there is a file Groups_in_Clifford.m stored in \Cliffordlib directory. It can be read into Maple 2017 as follows:

[>read(cat(savelibname,"/","Groups_in_Clifford.m"));

where 'savelibname' stores a path as a string to the \Cliffordlib directory, for example, savelibname = "D:\Maple2017/Cliffordlib". The value of savelibname is assigned in this new maple.ini file. Load and execute a worksheet "G03_as_central_product.mw" as an example.

WARNING: The above modification of maple.ini file is necessary as Maple 2017 cannot read files it saves unless both the "save" and the "read" commands contain the same complete path and a file name.

- cmulWalsh3 procedure to multiply Grassmann monomials in Cl(p,q) using Walsh functions is now fully functional. This means that via the command

[> useproduct(cmulWalsh3);

cmul can use internally cmulWalsh3 in Clifford algebras Cl(Q) of a non-degenerate quadratic form Q of signature (p,q). This procedure is part of Walshpackage. This package must be read in via the command

[> read(cat(savelibname,"/","Walshpackage.m"));

- A new help page on the entire Walshpackage is now included in Maple help system. Issue command

[> ?cmulWalsh3

to see Maple worksheet with the code of Walshpackage.

Please direct all questions, comments, and bug reports to:

Rafal Ablamowicz rablamowicz@tntech.edu

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DISCLAIMER: THERE IS NO WARRANTY FOR THE **CLIFFORD, Bigebra, Cliplus, Define, GfG, GTP, Octonion, RJGrobner, SchurFkt, SymGroupAlgebra, SP, Walshpackage, code_support **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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Last updated:
September 4, 2017
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