GrassmannCalculus`
ScalarParameter (★t)  |
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Details and Options
Examples
(2)
Basic Examples
(2)
In[1]:=
<<GrassmannCalculus`
The subscript pattern is one of the .
ScalarParameter
SpecialScalars
In[2]:=
 | SpecialScalars |
Out[2]=
★g,★n,,★λ,★0,,★c,_,
_,_,_
★σ
★t
(-1)
The following is an example of how the ScalarParameters arise from a specification of a plane in 3-space. Set Grassmann 3-space.
In[1]:=
 | SetCoordinateBoundVectorSpace |
Define a plane by three points.
In[2]:=
point1=★+;point2=★+-point1;point3=★+-point1;plane1=point1⋀point2⋀point3
e
x
e
y
e
z
Out[2]=
(★+)⋀(-+)⋀(-+)
e
x
e
x
e
y
e
x
e
z
A plane would be parametrized by two parameters, which means we can obtain a parametrization of the plane by dividing by a bivector consisting of two of the point in the expression. We do this with . This gives a parametrization that is in . (In order to define a parametrization for the plane we must convert the subscripted ScalarParameters to plain Symbols.)
plane1
ExteriorQuotient
plane1
In[3]:=
| ExteriorQuotient |
★t
1
★t
2
Out[3]=
★++(-+)+(-+)
e
x
e
x
e
y
★t
1
e
x
e
z
★t
2
Out[3]=
★++a(-+)+b(-+)
e
x
e
x
e
y
e
x
e
z
We check that the parametrization is in the plane.
In[4]:=
plane1⋀plane1Parametrization[a,b]//
| ZeroQ |
Out[4]=
True
In[5]:=
plane1Parametrization[1,1]
Out[5]=
★-++
e
x
e
y
e
z
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""