SamplePublisher`GrassmannCalculus`
PermuteExteriorFactors  |
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Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here the factors go to the positions. The sign of the mProduct is multiplied by the of the permutation. The canonical mVector is preserved.
{1,2,3,4,5,6}
{4,1,5,2,3,6}
Signature
In[2]:=
 | ★ℬ |
8
e
1
3
e
7
100
3
e
8
10
e
2
27
e
7
25
6
e
8
5
e
3
3
e
7
10
e
4
27
e
7
25
4
e
8
5
e
5
69
e
7
100
e
8
10
e
6
3
e
7
200
27
e
8
20
 | PermuteExteriorFactors |
| FastExteriorExpand |
| FastExteriorExpand |
Out[2]=
7+-⋀--⋀+⋀-+⋀++⋀--
e
1
3
e
7
100
3
e
8
10
e
2
27
e
7
25
6
e
8
5
e
3
3
e
7
10
e
4
27
e
7
25
4
e
8
5
e
5
69
e
7
100
e
8
10
e
6
3
e
7
200
27
e
8
20
Out[2]=
permutation{4,1,5,2,3,6}
Out[2]=
Signature-1
Out[2]=
7+-⋀--⋀+⋀-+⋀++⋀--
e
1
3
e
7
100
3
e
8
10
e
2
27
e
7
25
6
e
8
5
e
3
3
e
7
10
e
4
27
e
7
25
4
e
8
5
e
5
69
e
7
100
e
8
10
e
6
3
e
7
200
27
e
8
20
Out[2]=
-7--⋀-+⋀++⋀+-⋀+⋀--
e
2
27
e
7
25
6
e
8
5
e
4
27
e
7
25
4
e
8
5
e
5
69
e
7
100
e
8
10
e
1
3
e
7
100
3
e
8
10
e
3
3
e
7
10
e
6
3
e
7
200
27
e
8
20
Out[2]=
True
Symbolic vector Symbols can also be swapped.
In[3]:=
p⋀q⋀r⋀s⋀t⋀u%//
[{4,1,5,2,3,6}]
| PermuteExteriorFactors |
Out[3]=
p⋀q⋀r⋀s⋀t⋀u
Out[3]=
-(q⋀s⋀t⋀p⋀r⋀u)
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