GrassmannCalculus`
OrderInner  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
★A;
OrderInner sorts the arguments of an Inner product to Mathematica order. (Functions such as Subscript come after symbols.)
In[3]:=
⊖,x⊖,x⊖p,⊖
/@%
e
2
e
1
e
3
β
2
α
2
 | OrderInner |
Out[3]=
⊖,x⊖,x⊖p,⊖
e
2
e
1
e
3
β
2
α
2
Out[3]=
⊖,x⊖,p⊖x,⊖
e
1
e
2
e
3
α
2
β
2
In the following is not sorted because the factors have no defined grade and it is not recognized as an Inner product.
B⊖A
In[4]:=
b⊖a,((y⋀z)⊖(x⋀y))⊖a,⊖,B⊖A
/@%
z
6
y
6
| OrderInner |
Out[4]=
b⊖a,y⋀z⊖x⋀y⊖a,⊖,B⊖A
z
6
y
6
Out[4]=
a⊖b,a⊖(y⋀z⊖x⋀y),⊖,B⊖A
y
6
z
6
To arrive at a canonical form any exterior products must be ordered before using .
OrderInner
In[5]:=
(⋀)⊖(q⋀p)
/@%%//
%//
e
2
e
1
| OrderExterior |
| AggregateScalars |
| OrderInner |
Out[5]=
e
2
e
1
Out[5]=
-(⋀)⊖-(p⋀q)
e
1
e
2
Out[5]=
e
1
e
2
Out[5]=
p⋀q⊖⋀
e
1
e
2
That is the same result as given by .
GrassmannSimplify
In[6]:=
| ★ |
e
2
e
1
Out[6]=
p⋀q⊖⋀
e
1
e
2
 |
|
""