SamplePublisher`GrassmannCalculus`
ExteriorToSymmetrizedArray  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
SetEuclideanNSpace[4,{w,x,y,z},"Vector"]
The following are conversions of a vector and exterior products of various grades to symmetrized arrays.
In[3]:=
testVector=
[]
[testVector]Head[%]
 | RandomGrassmannVector |
 | ExteriorToSymmetrizedArray |
Out[3]=
-5++-5
e
w
e
x
e
y
e
z
Out[3]=
Out[3]=
StructuredArray
In[4]:=
testVector=First
[{1,6},1].
[2]
[testVector]MatrixForm[%]
 | RandomGrassmannMatrix |
 | GradeBasis |
| ExteriorToSymmetrizedArray |
Out[4]=
-10⋀-5⋀-5⋀-7⋀+3⋀-5⋀
e
w
e
x
e
w
e
y
e
w
e
z
e
x
e
y
e
x
e
z
e
y
e
z
Out[4]=
Out[4]//MatrixForm=
0 | -10 | -5 | -5 |
10 | 0 | -7 | 3 |
5 | 7 | 0 | -5 |
5 | -3 | 5 | 0 |
In[5]:=
testVector=First
[{1,4},1].
[3]step1=
[testVector]MatrixForm[step1]TensorSymmetry[step1]
| RandomGrassmannMatrix |
| GradeBasis |
| ExteriorToSymmetrizedArray |
Out[5]=
8⋀⋀-2⋀⋀+3⋀⋀-4⋀⋀
e
w
e
x
e
y
e
w
e
x
e
z
e
w
e
y
e
z
e
x
e
y
e
z
Out[5]=
Out[5]//MatrixForm=
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Out[5]=
Antisymmetric[{1,2,3}]
The following converts the last example back to a Grassmann 3-vector.
In[6]:=
| SymmetrizedArrayToExterior |
Out[6]=
8⋀⋀-2⋀⋀+3⋀⋀-4⋀⋀
e
w
e
x
e
y
e
w
e
x
e
z
e
w
e
y
e
z
e
x
e
y
e
z
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""