GrassmannCalculus`
ExtractBasisElements  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here is a list of the default basis elements of the algebra.
In[2]:=
★A;
 | GrassmannBases |
Out[2]=
{{1},{,,},{⋀,⋀,⋀},{⋀⋀}}
e
1
e
2
e
3
e
1
e
2
e
1
e
3
e
2
e
3
e
1
e
2
e
3
Here we compose a Grassmann number, and extract the basis elements.
In[3]:=
X=
[a]
 | ComposeGrassmannElement |
Out[3]=
a
0
a
1
e
1
a
2
e
2
a
3
e
3
a
4
e
1
e
2
a
5
e
1
e
3
a
6
e
2
e
3
a
7
e
1
e
2
e
3
In[4]:=
| ExtractBasisElements |
Out[4]=
{,,,⋀,⋀,⋀,⋀⋀}
e
1
e
2
e
3
e
1
e
2
e
1
e
3
e
2
e
3
e
1
e
2
e
3
Here is another Grassmann expression in a point space.
In[5]:=
| ★ |
3
e
1
e
2
e
1
 | ★ |
e
1
e
2
e
3
e
3
e
1
Here again we apply in a point space, but note that ⋀⋀ and ⋀ are also extracted even though they do not belong to .
ExtractBasisElements
e
1
e
2
e
1
e
3
e
1
GrassmannBases
In[6]:=
| ★ |
3
| GrassmannBases |
Out[6]=
{{1},{★,,,},{★⋀,★⋀,★⋀,⋀,⋀,⋀},{★⋀⋀,★⋀⋀,★⋀⋀,⋀⋀},{★⋀⋀⋀}}
e
1
e
2
e
3
e
1
e
2
e
3
e
1
e
2
e
1
e
3
e
2
e
3
e
1
e
2
e
1
e
3
e
2
e
3
e
1
e
2
e
3
e
1
e
2
e
3
In[7]:=
1-⋀⋀+2
⋀(⋀⊖)⋄(-2⋀)
e
1
e
2
e
1
 | ★ |
e
1
e
2
e
3
e
3
e
1
%//
| ExtractBasisElements |
Out[7]=
1+2★⋀(⋀⊖)⋄(-2⋀)-⋀⋀
e
1
e
2
e
3
e
3
e
1
e
1
e
2
e
1
Out[7]=
{★,,,⋀,⋀,⋀⋀}
e
1
e
3
e
1
e
2
e
3
e
1
e
1
e
2
e
1
In[8]:=
Clear[X]
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