Grassmann Algebra

TheExteriorProduct.nb 15
� Setting up a basis in GrassmannAlgebra
GrassmannAlgebra allows the setting up of an environment in which given symbols are
declared basis elements of � 1 . You can always see what your current basis is by entering Basis.
When first loaded, GrassmannAlgebra sets up a default basis:
Basis
�e1, e2, e3�
This is the basis of a 3-dimensional linear space which may be interpreted as a 3-dimensional
vector space if you wish.
To declare your own basis, enter DeclareBasis[list]. For example:
DeclareBasis��i, j, k��
�i, j, k�
Now, if we enter Basis we confirm that the current basis is the one we declared:
Basis
�i, j, k�
You can always return to the default basis by entering DeclareBasis[DefaultBasis],
or simply DeclareDefaultBasis[].
DeclareDefaultBasis��
�e1, e2, e3�
If you want a basis of higher dimension, include the dimension as an argument to
DeclareBasis. All default basis elements are of the form ei .
DeclareBasis�8�
�e1, e2, e3, e4, e5, e6, e7, e8�
An even shorter way of declaring such a basis is by entering the double-struck capital V
(�dsV�) subscripted with the dimension of the space required. This compact form is useful
in explorations involving frequent changes of basis.
2001 4 5
�5
�e1, e2, e3, e4, e5�