SamplePublisher`GrassmannCalculus`DifferentialGeometry`
GrassmannBundleSection  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Work in the GrassmannPlane.
In[2]:=
SetActiveAssociation
"Grassmann Plane"
[,]
 | PublicGrassmannAtlas |
 | ★★V |
The following evaluates a scalar expression at a specific point.
In[3]:=
(★+3+2)()%//
e
x
e
y
ℱ
⟺
y
x
| GrassmannBundleSection |
Out[3]=
(★+3+2)()
e
x
e
y
ℱ
⟺
y
x
Out[3]=
(★+3+2)(9)
e
x
e
y
ℱ
⟺
The following evaluates on a defined scalar function.
In[4]:=
| DefineScalarFunction |
y
x
e
x
e
y
ℱ
⟺
| GrassmannBundleSection |
Out[4]=
(★+3+2)(f1)
e
x
e
y
ℱ
⟺
Out[4]=
(★+3+2)(9)
e
x
e
y
ℱ
⟺
The following defines a tangent bundle over the Grassmann plane.
In[5]:=
| DefineScalarFunction |
| DefineScalarFunction |
ℱ
⟺
e
x
e
y
| InsertPosition |
| GrassmannBundleSection |
Out[5]=
()(f1+f2)
ℱ
⟺
e
x
e
y
Out[5]=
(★+x+y)(f1+f2)
e
x
e
y
ℱ
⟺
e
x
e
y
Out[5]=
(★+x+y)(xy+(x+y))
e
x
e
y
ℱ
⟺
e
x
e
y
The following gives the tangent vector at a specific point using from above.
step1
In[6]:=
step1/.★+3-2%//
e
x
e
y
| GrassmannBundleSection |
Out[6]=
(★+3-2)(f1+f2)
e
x
e
y
ℱ
⟺
e
x
e
y
Out[6]=
(★+3-2)(-6+)
e
x
e
y
ℱ
⟺
e
x
e
y
In[7]:=
Clear[f1,f2,step1]
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""