Grassmann Algebra

Preface.nb 3
Chapters 7 to 13: Exploring Screw Algebra, Mechanics, Grassmann Algebra, The Generalized
Product, Hypercomplex Algebra, Clifford Algebra, and Grassmann Matrix Algebra, may be
read independently of each other, with the proviso that the chapters on hypercomplex and
Clifford algebra depend on the notion of the generalized product.
Sections within the text which use GrassmannAlgebra or Mathematica are signified with the
Mathematica icon �. Wherever possible, explanation is provided so that the results are still
intelligible without a knowledge of Mathematica. Mathematica input/output dialogue is in
indented Courier font, with the input in bold. For example:
Expand��x � y� 3 �
x 3 � 3x 2 y � 3xy 2 � y 3
The Guide to GrassmannAlgebra is a summary of the most important functions of the
GrassmannAlgebra package. This may be used as an overview of the package capabilities or as
a 'Quick Start' guide.
The GrassmannAlgebra website
As with most books these days, this book has its own website: www.GrassmannAlgebra.xxx.zz.
On this site you will find, amongst other things, errata, additional material, upgrades to the
GrassmannAlgebra package, links to other Grassmann algebra sites, notification of new or
related editions, reviews and my email address.
Acknowledgements
Finally I would like to acknowledge those who were instrumental in the evolution of this book:
Cecil Pengilley who originally encouraged me to look at applying Grassmann's work to
engineering; the University of Melbourne, University of Rochester and Swinburne University of
Technology which sheltered me while I pursued this interest; Janet Blagg who peerlessly edited
the text; my family who had to put up with my writing, and finally to Stephen Wolfram who
created Mathematica and provided me with a visiting scholar's grant to work at Wolfram
Research Institute in Champaigne where I began developing the GrassmannAlgebra package.
Above all however, I must acknowledge Hermann Grassmann. His contribution to mathematics
and science puts him among the great thinkers of the nineteenth century.
I hope you enjoy exploring this beautiful mathematical system.
2001 4 5
For I have every confidence that the effort I have applied to the science reported upon
here, which has occupied a considerable span of my lifetime and demanded the most
intense exertions of my powers, is not to be lost. É a time will come when it will be
drawn forth from the dust of oblivion and the ideas laid down here will bear fruit. É some
day these ideas, even if in an altered form, will reappear and with the passage of time will
participate in a lively intellectual exchange. For truth is eternal, it is divine; and no phase
in the development of truth, however small the domain it embraces, can pass away without
a trace. It remains even if the garments in which feeble men clothe it fall into dust.