GrassmannCalculus`
CommonFactorTheoremA  |
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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 , is able to decompose the first factor in order to perform the expansion. We show the Precedence.
(x⋀y)⋁
β
2
CommonFactorTheoremA
In[2]:=
★A;
;A=
(x⋀y)⋁
 | ★P |
| CommonFactorTheoremA |
β
2
Out[2]=
(x⋀)⋁y+(y⋀)⋁(-x)
β
2
β
2
CommonFactorTheoremA
In[3]:=
| ★ℬ |
4
 | ComposeSimpleForm |
α
3
| ComposeSimpleForm |
β
2
Out[3]=
(⋀⋀)⋁(⋀)
α
1
α
2
α
3
β
1
β
2
In[4]:=
 | CommonFactorTheoremA |
Out[4]=
(⋀⋀⋀)⋁+(⋀⋀⋀)⋁(-)+(⋀⋀⋀)⋁
α
1
α
2
β
1
β
2
α
3
α
1
α
3
β
1
β
2
α
2
α
2
α
3
β
1
β
2
α
1
However, if it cannot expand by decomposing the first factor, it will try to expand by decomposing the second factor.
In[5]:=
| ★ℬ |
4
| CommonFactorTheoremA |
α
2
Out[5]=
(⋀(-(x⋀z)))⋁y+(⋀x⋀y)⋁z+(⋀y⋀z)⋁x
α
2
α
2
α
2
In[6]:=
| ★★P |
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