SamplePublisher`GrassmannCalculus`
VectorSpaceComplements  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
savePreferences=
;
 | AllPreferences |
Set the GrassmannPlane.
In[3]:=
SetPreferences["GrassmannPlane","Vector"]
The following generates the vector space complements of all the basis vectors and then processes them. The never appears under an but can appear under an .
Origin
OverVector
OverBar
In[4]:=
 | GrassmannBases |
 | VectorSpaceComplements |
| ToGrassmannComplements |
| ConvertComplements |
Out[4]=
{{1},{★,,},{★⋀,★⋀,⋀},{★⋀⋀}}
e
x
e
y
e
x
e
y
e
x
e
y
e
x
e
y
Out[4]=
★⋀,,-(★⋀),-★⋀,,,★⋀⋀,⋀
1
1
e
x
e
y
e
x
e
y
e
x
e
y
e
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e
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Out[4]=
{},,,,,,⋀,
1
★
e
x
e
y
★⋀
e
x
★⋀
e
y
e
x
e
y
★⋀⋀
e
x
e
y
Out[4]=
{{★⋀⋀},{⋀,-(★⋀),★⋀},{,-,★},{1}}
e
x
e
y
e
x
e
y
e
y
e
x
e
y
e
x
The following generates a general Grassmann element in the space and takes the vector space complement.
In[5]:=
| ComposeGrassmannElement |
| VectorSpaceComplements |
Out[5]=
c
0
c
1
c
2
e
x
c
3
e
y
c
4
e
x
c
5
e
y
c
6
e
x
e
y
c
7
e
x
e
y
Out[5]=
1
c
1
e
x
c
4
e
y
c
5
e
x
e
y
c
7
c
0
1
c
2
e
x
c
3
e
y
c
6
e
x
e
y
The following sets up a non-bound book vector space. Using VectorSpaceComplements generates warning messages and leaves the expression unchanged.
In[6]:=
★A;
;
[%]
| ★ℬ |
2
| GrassmannBases |
| VectorSpaceComplements |
Out[6]=
{{1},{,},{⋀}}
e
1
e
2
e
1
e
2
Out[6]=
{{1},{,},{⋀}}
e
1
e
2
e
1
e
2
In[7]:=
| RestorePreferences |
 |
|
""