Grassmann Algebra

TheExteriorProduct.nb 6
At any stage you can declare extra scalars and have them added to the list of currently declared
scalars. (More precisely, it is the union of the current list and the new list that becomes the
declared list.) For example:
DeclareExtraScalars��a, aa, aaa��
�a, aa, aaa, b, c, d, e, f, g, h, �, �_ � _�? InnerProductQ, _� 0
You can use patterns in the list of declared scalars. For example, you may wish to declare all
subscripted symbols with the kernel symbol Α as scalars.
DeclareExtraScalars��Α_ ��
�a, aa, aaa, b, c, d, e, f, g,
h, �, �_ � _� ?InnerProductQ, Α_, _� 0
We can check if a given element is a scalar, or all the elements in a list are scalars, with
ScalarQ.
ScalarQ��Α_ , Α2, Αnew ,x���� y, x 0 ,x��
�True, True, True, True, True, False�
� Entering exterior products
The exterior product is symbolized by the wedge '�'. This may be entered either by typing \[
Wedge], by typing the alias �^�, or by clicking on the � button on the palette.
As an infix operator, x�y�z�� is interpreted as Wedge[x,y,z,�].
To enter x�y type x�^�y, or click the ��� button on the palette. The first placeholder will
be selected automatically for immediate typing. To move to the next placeholder, press the tab
key. To produce a multifactored exterior product, click the palette button as many times as
required. To take the exterior product with an existing expression, select the expression and
click the ��� button.
For example, to type (x+y)�(x+z), first type (x+y) and select it, click the ��� button, then
type (x+z).
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