Below is a sample of help pages available for 'CLIFFORD',
and four supplementary packages: 'Cli5plus', 'Bigebra',
and 'Octonion'. Each procedure in each package
is well documented via an on-line database consisting of hyper linked help
pages. These help pages are reachable from the Maple prompt and through
the Maple browser. Some of these pages have been converted to .html format
(using Maple's built-in export to HTML feature) and are available below.
||Department of Mathematics
Tennessee Technological University
Sample Help Pages for
'CLIFFORD - A Maple V (R. 5) Package for Clifford Algebra Computations'
'Bigebra' - Package for computations with Hopf algebras (version
'GTP' - Package for computations with graded tensor products of
Clifford algebras (version 5)
'Octonion' - Package for computations with octonions (version 4)
'Cli5plus' - Package that extends certain features of 'CLIFFORD'
Rafal Ablamowicz (*) and Bertfried Fauser (**)
(*) Department of Mathematics, Box 5054
(**) Universität Konstanz, Fachbereich Physik, Fach M678
Tennessee Technological University, Cookeville, TN 38505
phone: USA (931) 372-3569, fax: USA (931) 372-6353
78457 Konstanz, Germany
Permission is given to download these files as long as they are for
individual use and not for distribution of any kind including posting these
files on any other server but this one. All help pages are copyrighted
by Rafal Ablamowicz and Bertfried Fauser.
You can find out how I use CLIFFORD by going to my
recent publications page.
SAMPLE HELP PAGES FOR 'CLIFFORD' (VERSION
Main introductory help page Cliff5[intro].
Procedure that displays environmental variables used by all packages is
Clifford multiplication procedure cmul.
Internal Clifford multiplication procedure cmulNUM
using recursive definition of Chevalley.
Internal Clifford multiplication procedure cmulRS
using Rota-Stein cliffordization procedure.
Reversion in Clifford algebra Cl(B) using B dependent reversion.
One of two procedures that gives a scalar product in a spinor space considered
as a minimal left ideal is beta_plus.
Matrix representations of Clifford algebras are accomplished with the procedure
Multiplication of Clifford matrices is done with rmulm.
Computation of a spinor basis in a minimal left or right ideal is done
Determination if a Clifford matrix is a Vahlen matrix is done with isVahlenmatrix.
Rotation in three dimensions accomplished with quaternions and a procedure
Exterior wedge multiplication is done with wedge.
Clifford exponentiation is done with sexp
modulo a minimal polynomial.
SAMPLE HELP PAGES FOR 'Cli5plus' (VERSION
Dotted wedge procedure dwedge.
extends B dependent reversion in Cl(B) to the Clifford basis.
Multiplication procedure climul
extends Clifford product to the Clifford basis.
converts Clifford polynomials from an undotted wedge basis to a dotted
SAMPLE HELP PAGES FOR 'Bigebra' (VERSION
SAMPLE HELP PAGES FOR 'GTP' (VERSION
Clifford product in Clifford algebras Cl(B1), Cl(B2), ..., Cl(Bn) is done
Basis in the graded tensor product is defined with gbasis.
Multiplication in the graded tensor product of Clifford algebras is accomplished
SAMPLE HELP PAGES FOR 'OCTONION' (VERSION
User may define an octonion multiplication table with def_omultable.
Octonion multiplication is done with omul.
Octonionic norm is computed with onorm.
Octonionic multiplication is defined in terms of Fano_triples
which are related to the Fano plane.
Please direct all questions, comments, and reports on bugs to:
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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CLIFFORD's home page
Last updated: January 5, 2002/ra