GrassmannCalculus`
Dual  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | Dual |
α
m
β
m+k
 | Λ |
m+k
Out[2]=
,,
α
m
β
-★n+k+m
Λ
-★n+k+m
Exploration.
Standard theorem
In[3]:=
∈
,∈
⟹⋀∈
[%]
α
m
 | Λ |
m
β
k
| Λ |
k
α
m
β
k
| Λ |
m+k
| Dual |
Out[3]=
∈,∈⟹⋀∈
α
m
Λ
m
β
k
Λ
k
α
m
β
k
Λ
k+m
Out[3]=
∈,∈⟹⋁∈
α
m
Λ
m
β
k
Λ
k
α
m
β
k
Λ
-★n+k+m
Oldball theorem with sum of grades
In[4]:=
∈
,∈
⟹⋀∈
[%]
α
m
| Λ |
m
β
m+k
| Λ |
m+k
α
m
β
m+k
| Λ |
2m+k
| Dual |
Out[4]=
∈,∈⟹⋀∈
α
m
Λ
m
β
k+m
Λ
k+m
α
m
β
k+m
Λ
k+2m
Out[4]=
∈,∈⟹⋁∈
α
m
Λ
m
β
-★n+k+m
Λ
-★n+k+m
α
m
β
-★n+k+m
Λ
k-2(★n-m)
Numeric grade
In[5]:=
∈
,∈
⟹⋀∈
[%]
α
m
| Λ |
m
β
3
| Λ |
3
α
m
β
3
| Λ |
m+3
| Dual |
Out[5]=
∈,∈⟹⋀∈
α
m
Λ
m
β
3
Λ
3
α
m
β
3
Λ
3+m
Out[5]=
∈,∈⟹⋁∈
α
m
Λ
m
β
-3+★n
Λ
-3+★n
α
m
β
-3+★n
Λ
-3+m
Both numeric grade. These all work.
In[6]:=
 | ★ℬ |
6
In[7]:=
∈
,∈
⟹⋀∈
[%]%/.
6
[%]/.
6
α
2
| Λ |
2
β
3
| Λ |
3
α
2
β
3
| Λ |
5
| Dual |
| ★n |
| Dual |
| ★n |
Out[7]=
∈,∈⟹⋀∈
α
2
Λ
2
β
3
Λ
3
α
2
β
3
Λ
5
Out[7]=
∈,∈⟹⋁∈
α
-2+★n
Λ
-2+★n
β
-3+★n
Λ
-3+★n
α
-2+★n
β
-3+★n
Λ
-5+★n
Out[7]=
∈,∈⟹⋁∈
α
4
Λ
4
β
3
Λ
3
α
4
β
3
Λ
1
Out[7]=
∈,∈⟹⋀∈
α
2
Λ
2
β
3
Λ
3
α
2
β
3
Λ
5
 |
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