GrassmannCalculus`
InnerProductQ  |
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
InnerProductQ
Listable
In[2]:=
★A;
⊖⊖y
 | InnerProductQ |
x
⊖x,x
2
z
3
Out[2]=
{True,True}
Here is a slightly more complex inner product in a 4-space. Turn on Precedence formatting. The expression reduces to an interior product with a grade 2 expression on each side.
In[3]:=
| ★ℬ |
4
 | ★P |
e
4
w
2
e
2
| ★★P |
| InnerProductQ |
[
%]Out[3]=
(⋀(s+t))⊖(u⋀((x⋀y)⊖(z-⊖)))
e
4
w
2
e
2
Out[3]=
True
However, if the dimension of the space is 3, is no longer a basis element (hence not a Grassmann symbol), and returns .
e
4
InnerProductQ
False
In[4]:=
| ★ℬ |
3
| InnerProductQ |
[
e
4
w
2
e
2
Out[4]=
False
 |
|
 |
|
""