Grassmann Algebra

9 Grassmann Algebra
9.1 Introduction
9.2 Grassmann Numbers
� Creating Grassmann numbers
� Body and soul
� Even and odd components
� The grades of a Grassmann number
� Working with complex scalars
9.3 Operations with Grassmann Numbers
� The exterior product of Grassmann numbers
� The regressive product of Grassmann numbers
� The complement of a Grassmann number
� The interior product of Grassmann numbers
9.4 Simplifying Grassmann Numbers
� Elementary simplifying operations
� Expanding products
� Factoring scalars
� Checking for zero terms
� Reordering factors
� Simplifying expressions
9.5 Powers of Grassmann Numbers
� Direct computation of powers
� Powers of even Grassmann numbers
� Powers of odd Grassmann numbers
� Computing positive powers of Grassmann numbers
� Powers of Grassmann numbers with no body
� The inverse of a Grassmann number
� Integer powers of a Grassmann number
� General powers of a Grassmann number
9.6 Solving Equations
� Solving for unknown coefficients
� Solving for an unknown Grassmann number
9.7 Exterior Division
� Defining exterior quotients
� Special cases of exterior division
� The non-uniqueness of exterior division
9.8 Factorization of Grassmann Numbers
The non-uniqueness of factorization
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