SamplePublisher`GrassmannCalculus`
ScaleProductElementValue  |
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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
Scale the second factor so the coefficient of is .
e
4
1
In[3]:=
mProduct2=mProduct//
[{2,}]canonicalMVector2=
[mProduct2]canonicalMVector2canonicalMVector
 | ScaleProductElementValue |
e
4
| FastExteriorExpand |
Out[3]=
15
4
e
1
3
e
4
8
e
5
2
8
e
2
3
e
4
4
e
5
21
e
3
e
5
7
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
Scale the third factor so the coefficient of is -3.
e
5
In[4]:=
mProduct2=mProduct//
[{3,},-3]canonicalMVector2=
[mProduct2]canonicalMVector2canonicalMVector
| ScaleProductElementValue |
e
5
| FastExteriorExpand |
Out[4]=
10
21
e
1
3
e
4
8
e
5
2
e
2
3
e
4
8
e
5
14
e
3
e
5
Out[4]=
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[4]=
True
And it works with some other products.
In[5]:=
mProduct/.WedgeCircleDot%//
[{3,},-3]
| ScaleProductElementValue |
e
5
Out[5]=
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[5]=
10
21
e
1
3
e
4
8
e
5
2
e
2
3
e
4
8
e
5
14
e
3
e
5
 |
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