SamplePublisher`GrassmannCalculus`
ScaleProductFactor  |
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Details
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 by 3. When expanded to canonical form the result is equal to the original vector.
In[3]:=
mProduct2=mProduct//
[2,3]canonicalMVector2=
[mProduct2]canonicalMVector2canonicalMVector
 | ScaleProductFactor |
| FastExteriorExpand |
Out[3]=
10
3
e
1
3
e
4
8
e
5
2
e
2
9
e
4
8
3
e
5
14
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
This also works for symbolic products.
In[4]:=
product=3p⋀q⋀r
[1,a][product]
[%]
| ScaleExteriorFactor |
 | ★ |
Out[4]=
3p⋀q⋀r
Out[4]=
3(ap)⋀q⋀r
a
Out[4]=
3p⋀q⋀r
It also works on certain undefined product operators.
In[5]:=
mProduct/.WedgeCirclePlus%//
[2,3]
| ScaleProductFactor |
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
3
e
1
3
e
4
8
e
5
2
e
2
9
e
4
8
3
e
5
14
e
3
e
5
7
 |
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