Files IIPR.TXT, IIMT.TXT, and ONBS.TXT contain FORTRAN programs whose 
theoretical background is described in:

"ORTHONORMAL BASIS SETS IN CLIFFORD ALGEBRAS"
G. Bergdolt
Centre de Recherches Nucleaires, C.N.R.S.
B.P.28
F-67037 Strasbourg Cedex-2, France
e-mail: BERGDOLT@frcpn11.in2p3.fr

in

Title: ``Clifford Algebras with Numeric and Symbolic Computations''
Editors: Rafal Ablamowicz, Pertti Lounesto, Josep M. Parra
ISBN: 0-8176-3907-1
PUBLISHER: Birkhauser, Boston
YEAR: 1996

Copyright is reserved but permission is given to download the files for
individual use. 

Foreword: Real vector spaces of neutral signature (p=q) admit bases
formed by dual sets of isotropic vectors. The Clifford algebras over
these spaces admit bases formed by ordered products of isotropic
vectors. Projectors are elements of the Clifford algebra satisfying
the product relations of matrix units. A set of projectors can be
constructed forming a basis of the algebra. The programs IIPR and IIMT
compute the expansion of ordered products in projectors. This amounts
to compute a matrix realisation of the neutral Clifford algebra.
Since any simple real Clifford algebra is isomorphic to the tensor
product of a neutral Clifford algebra and a Clifford algebra of
type Cl(0,0),Cl(0,1) or Cl(0,2) isomorphic to the fields R,C or H,
the program allows the construction of matrix algebras with entries
in R,C or H isomorphic to any real simple Clifford algebra.
The program ONBS computes orthogonal basis sets of Clifford algebras.
Orthogonal basis sets are sets of multivectors satisfying the
scalar product relations with a given signature. Orthonormal basis
sets define isomorphisms and automorphisms in real Clifford algebras.

Title      Type  Lines   Description
IIPR.TXT   ASCII 49      Computes the expansion of ordered products in
																									projectors (matrix units).
IIMT.TXT   ASCII 41      Computes matrices isomorphic to ordered products
																									of isotropic vectors.
ONBS.TXT   ASCII 172     Determines independant orthonormal basis sets for
																									Clifford algebras.
Usage notes: The files are Fortran VS programs using the bit handling
subroutines IAND, IEOR, ISHFT, BTEST and IBSET( VS Fortran Language
Reference, Appendix B, IBM). The DATA IMP/32/ instruction in the programs
sets the logical unit label corresponding to the output file. In the
VM operating system used there is a corresponding Filedef instruction.
In the program IIPR the input data is MD defining the signature MD=p=q.
Md is introduced by the DATA instruction DATA MD/2/ and can be changed.
The Format instructions allow values MD less or equal to 13, but the
computing time and output volume sets much lower limits.
The program IIMT performs the same computations but the result is
presented in matrix form, hence the program requires an array of
4**MD. The input data MD is introduced via a PARAMETER instruction.
In the output file the ordered products are defined by twoo labels as
described in the paper.

The input for the program ONBS is ND the dimension of the underlying
vector space introduced by a DATA instruction. Two flags KFA and KFB are
also set by DATA instructions. If KFA is set to 1 the inverse of the ONB
matrices are printed, if KFB is set to 1 the squares of the multivectors
are printed for all sign combination of the squares of basis vectors.
The sign combinations of the latter are labelled by an index and printed
under the trivial ONB formed by the basis vectors.

End of file
