GrassmannCalculus`
ToGrassmannComplements  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set the Grassmann Plane coordinate system.
In[2]:=
SetActiveAssociation
"Grassmann Plane"
 | PublicGrassmannAtlas |
Write an expression with vector space complements.
In[3]:=
★+★⋀+
[%]%//
e
x
1+++x⋀
e
x
e
y
e
x
e
y
 | ToGrassmannComplements |
| ConvertComplements |
Out[3]=
★++★⋀
1+++x⋀
e
x
e
y
e
x
e
y
e
x
Out[3]=
★++++x+★⋀
★
★⋀
e
x
★⋀
e
y
★⋀⋀
e
x
e
y
e
x
Out[3]=
x-++★⋀(1+)+⋀
e
x
e
y
e
x
e
x
e
y
ConvertCcomplements further simplified the expression, and would directly simplify the vector space complement expression.
In[4]:=
★+★⋀+%//
e
x
1+++x⋀
e
x
e
y
e
x
e
y
| ConvertComplements |
Out[4]=
★++★⋀
1+++x⋀
e
x
e
y
e
x
e
y
e
x
Out[4]=
x-++★⋀(1+)+⋀
e
x
e
y
e
x
e
x
e
y
The following would be an improper expression because the should only apply to the vector subspace elements. will not convert it.
VectorSpaceComplement
ToGrassmannComplements
In[5]:=
★⋀
e
x
| ToGrassmannComplements |
Out[5]=
★⋀
e
x
Out[5]=
★⋀
e
x
The following is proper.
In[6]:=
★⋀%//
%//
e
x
| ToGrassmannComplements |
| ConvertComplements |
Out[6]=
★⋀
e
x
Out[6]=
-
e
x
Out[6]=
★⋀
e
y
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""