SamplePublisher`GrassmannCalculus`
SwapExteriorFactors  |
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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
Swap the first and third factors. This also changes the sign of the leading coefficient and maintains the value of the multi-vector.
In[3]:=
multivector2=multivector//
[{1,3}]canonicalMVector2=
[multivector2]canonicalMVector2canonicalMVector
 | SwapExteriorFactors |
| FastExteriorExpand |
Out[3]=
-10-⋀++⋀++
e
3
e
5
7
e
2
3
e
4
8
e
5
14
e
1
3
e
4
8
e
5
2
Out[3]=
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
Out[3]=
True
Symbolic vector Symbols can also be swapped.
In[4]:=
p⋀q⋀r%//
[{1,2}]
| SwapExteriorFactors |
Out[4]=
p⋀q⋀r
Out[4]=
-(q⋀p⋀r)
This can also be used to order two products so they can be . The common factor must be in the last slot for both terms.
Condensed
In[5]:=
p⋀q⋀r+s⋀r⋀tMapAt
[{2,3}],%,2%//
| SwapExteriorFactors |
 | Condense |
Out[5]=
p⋀q⋀r+s⋀r⋀t
Out[5]=
p⋀q⋀r-s⋀t⋀r
Out[5]=
(p⋀q-s⋀t)⋀r
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""