SamplePublisher`GrassmannCalculus`
PivotExteriorProduct  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
The following is a 3-vector in 5-space with its expanded canonical 3-vector.
In[2]:=
 | ★ℬ |
5
e
1
3
e
4
8
e
5
2
e
2
3
e
4
8
e
5
14
e
3
e
5
7
| FastExteriorExpand |
Out[2]=
10++⋀++⋀-
e
1
3
e
4
8
e
5
2
e
2
3
e
4
8
e
5
14
e
3
e
5
7
Out[2]=
10⋀⋀-⋀⋀-⋀⋀-⋀⋀-⋀⋀+⋀⋀+5⋀⋀+⋀⋀-⋀⋀
e
1
e
2
e
3
10
7
e
1
e
2
e
5
15
4
e
1
e
3
e
4
5
7
e
1
e
3
e
5
15
28
e
1
e
4
e
5
15
4
e
2
e
3
e
4
e
2
e
3
e
5
15
28
e
2
e
4
e
5
45
28
e
3
e
4
e
5
Here we do a single pivot on in the second factor. ends with a coefficient of in the second factor and is missing in all the other factors.
e
5
e
5
1
In[3]:=
mProduct2=mProduct//
[{2,}]
[mProduct2]canonicalMVector
 | PivotExteriorProduct |
e
5
| FastExteriorExpand |
Out[3]=
5
7
e
1
e
2
9
e
4
4
e
2
21
e
4
4
e
5
e
2
e
3
3
e
4
4
Out[3]=
True
Here we pivot on in the first factor, in the second factor and in the third factor to 'diagonalize' a product on these Basis vectors.
e
1
e
4
e
5
In[4]:=
mProductresult2=mProduct//
[{1,}]result3=result2//
[{2,}]result4=result3//
[{3,}]
[mProduct]
[result2]
[result3]
[result4]
| PivotExteriorProduct |
e
1
| PivotExteriorProduct |
e
4
| PivotExteriorProduct |
e
5
| FastExteriorExpand |
| FastExteriorExpand |
| FastExteriorExpand |
| FastExteriorExpand |
Out[4]=
10++⋀++⋀-
e
1
3
e
4
8
e
5
2
e
2
3
e
4
8
e
5
14
e
3
e
5
7
Out[4]=
10++⋀++⋀-
e
1
3
e
4
8
e
5
2
e
2
3
e
4
8
e
5
14
e
3
e
5
7
Out[4]=
15
4
e
1
e
2
3
e
5
7
8
e
2
3
e
4
4
e
5
21
e
3
e
5
7
Out[4]=
-(-+3)⋀++⋀(-7+)
15
28
e
1
e
2
e
3
8
e
2
3
4
e
3
3
e
4
e
3
e
5
Out[4]=
True
Diagonalization can also be performed with .
ToReducedFactoredForm
In[5]:=
 | ToReducedFactoredForm |
e
1
e
4
e
5
Out[5]=
-(-+3)⋀++⋀(-7+)
15
28
e
1
e
2
e
3
8
e
2
3
4
e
3
3
e
4
e
3
e
5
 |
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