GrassmannCalculus`
ConvertCliffordToGeneralized  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
★A;
;
 | ★ℬ |
4
 | ★P |
The generalized product is the pathway to the customary expression in terms of exterior and interior products.
In[3]:=
p⋄q%//
%//
| ConvertCliffordToGeneralized |
| ConvertGeneralizedToInterior |
Out[3]=
p⋄q
Out[3]=
pq+pq
△
0
△
1
Out[3]=
p⊖q+p⋀q
In[4]:=
★A;
;
⋄%//
%//
| ★ℬ |
6
| ★P |
α
2
β
4
| ConvertCliffordToGeneralized |
| ConvertGeneralizedToInterior |
Out[4]=
α
2
β
4
Out[4]=
α
2
△
0
β
4
α
2
△
1
β
4
α
2
△
2
β
4
Out[4]=
-⊖+(⊖)⋀-(⊖)⋀+⋀
β
4
α
2
β
4
α
2
α
3
β
4
α
3
α
2
β
4
α
2
In this expression some simplification can be performed as the last term is zero.
In[5]:=
α
3
β
4
| ConvertCliffordToGeneralized |
| SimplifyGeneralizedProducts |
| ConvertGeneralizedToInterior |
Out[5]=
α
3
β
4
Out[5]=
α
3
△
0
β
4
α
3
△
1
β
4
α
3
△
2
β
4
α
3
△
3
β
4
Out[5]=
-⊖+-
β
4
α
3
α
3
△
1
β
4
α
3
△
2
β
4
Out[5]=
-⊖-(⊖(⋀))⋀+(⊖(⋀))⋀-(⊖(⋀))⋀+(⊖)⋀⋀-(⊖)⋀⋀+(⊖)⋀⋀
β
4
α
3
β
4
α
4
α
5
α
6
β
4
α
4
α
6
α
5
β
4
α
5
α
6
α
4
β
4
α
4
α
5
α
6
β
4
α
5
α
4
α
6
β
4
α
6
α
4
α
5
When metric elements are present will use . may further simplify.
SimplifyGeneralizedProducts
ConvertGeneralizedToInterior
ToMetricElements
In[6]:=
e
3
e
2
e
4
| ConvertCliffordToGeneralized |
| SimplifyGeneralizedProducts |
| ToMetricElements |
Out[6]=
e
3
e
2
e
4
Out[6]=
e
3
△
0
e
2
e
4
e
3
△
1
e
2
e
4
Out[6]=
(⋀)⊖-⋀⋀
e
2
e
4
e
3
e
2
e
3
e
4
Out[6]=
-(⋀⋀)
e
2
e
3
e
4
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