GrassmannCalculus`
ConvertGeneralizedToInteriorB  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
★A;
;
 | ★ℬ |
4
 | ★P |
The two forms of converting generalized products to interior and exterior products sometimes give the same result.
In[3]:=
step1=Tablep
q,{i,0,2}step1//
step1//
 | △ |
i
| ConvertGeneralizedToInterior |
| ConvertGeneralizedToInteriorB |
Out[3]=
pq,pq,pq
△
0
△
1
△
2
Out[3]=
{p⋀q,p⊖q,0}
Out[3]=
{p⋀q,p⊖q,0}
In this case some of the results are different.
In[4]:=
★A;
;step1=Table
,{i,0,2}step1//
step1//
| ★ℬ |
6
α
3
| △ |
i
β
2
| ConvertGeneralizedToInterior |
| ConvertGeneralizedToInteriorB |
Out[4]=
,,
α
3
△
0
β
2
α
3
△
1
β
2
α
3
△
2
β
2
Out[4]=
⋀,(⊖)⋀-(⊖)⋀,⊖
α
3
β
2
α
3
β
2
β
3
α
3
β
3
β
2
α
3
β
2
Out[4]=
⋀,-(⋀)⊖+(⋀)⊖,⊖
α
3
β
2
α
3
β
2
β
3
α
3
β
3
β
2
α
3
β
2
In[5]:=
★A;
;step1=Table
,{i,0,2}step1//
step1//
| ★ℬ |
6
α
3
| △ |
i
β
3
| ConvertGeneralizedToInterior |
| ConvertGeneralizedToInteriorB |
Out[5]=
,,
α
3
△
0
β
3
α
3
△
1
β
3
α
3
△
2
β
3
Out[5]=
⋀,(⊖)⋀⋀-(⊖)⋀⋀+(⊖)⋀⋀,(⊖(⋀))⋀-(⊖(⋀))⋀+(⊖(⋀))⋀
α
3
β
3
α
3
β
4
β
5
β
6
α
3
β
5
β
4
β
6
α
3
β
6
β
4
β
5
α
3
β
4
β
5
β
6
α
3
β
4
β
6
β
5
α
3
β
5
β
6
β
4
Out[5]=
⋀,(⋀⋀)⊖-(⋀⋀)⊖+(⋀⋀)⊖,(⋀)⊖(⋀)-(⋀)⊖(⋀)+(⋀)⊖(⋀)
α
3
β
3
α
3
β
4
β
5
β
6
α
3
β
4
β
6
β
5
α
3
β
5
β
6
β
4
α
3
β
4
β
5
β
6
α
3
β
5
β
4
β
6
α
3
β
6
β
4
β
5
In[6]:=
| ★★P |
 |
|
 |
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