GrassmannCalculus`
CommonFactorTheoremB  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
We choose a 3-space and consider the regressive product of two 2-elements, one of which is explicitly expressed as an exterior product, while the other is a general 2-element.
When the product is expressed as ⋁(x⋀y), is able to decompose the second factor in order to perform the expansion.
β
2
CommonFactorTheoremB
In[2]:=
★A;
;B=
⋁(x⋀y)
 | ★P |
 | CommonFactorTheoremB |
β
2
Out[2]=
(⋀(-x))⋁y+(⋀y)⋁x
β
2
β
2
CommonFactorTheoremB
In[3]:=
 | ★ℬ |
4
 | ComposeSimpleForm |
α
2
| ComposeSimpleForm |
β
3
Out[3]=
(⋀)⋁(⋀⋀)
α
1
α
2
β
1
β
2
β
3
In[4]:=
| CommonFactorTheoremB |
Out[4]=
(⋀⋀(-(⋀)))⋁+(⋀⋀⋀)⋁+(⋀⋀⋀)⋁
α
1
α
2
β
1
β
3
β
2
α
1
α
2
β
1
β
2
β
3
α
1
α
2
β
2
β
3
β
1
However, if it cannot expand by decomposing the second factor, it will try to expand by decomposing the first factor.
In[5]:=
| ★ℬ |
4
| CommonFactorTheoremB |
α
2
Out[5]=
(x⋀y⋀)⋁z+(x⋀z⋀)⋁(-y)+(y⋀z⋀)⋁x
α
2
α
2
α
2
In[6]:=
★A;
;Clear[B,F]
| ★★P |
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""