SamplePublisher`GrassmannCalculus`DifferentialGeometry`
GrassmannBundle  |
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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 is a symbolic form of a . It can be entered in either form.
GrassmannBundle
In[3]:=
[,],()()
 | GrassmannBundle |
ℱ
⟺
Out[3]=
()(),()()
ℱ
⟺
ℱ
⟺
The following is a specific vector at a specific point in the Grassmann plane. The left entry is a point in the Grassmann plane and the right entry is a vector in the tangent space attached to that point.
In[4]:=
(★+3+4)(2-)
e
x
e
y
ℱ
⟺
e
x
e
y
Out[4]=
(★+3+4)(2-)
e
x
e
y
ℱ
⟺
e
x
e
y
The following is a scalar function on a parametric curve in the Grassmann plane.
In[5]:=
(★+αx[t]+αy[t])(αx[t])
e
x
e
y
ℱ
⟺
2
αy[t]
Out[5]=
(★+αx[t]+αy[t])(αx[t])
e
x
e
y
ℱ
⟺
2
αy[t]
The following is the tangent bundle to the same curve in the Grassmann plane.
In[6]:=
position[t_]:=★+αx[t]+αy[t];(position[t])(position'[t])
e
x
e
y
ℱ
⟺
Out[6]=
(★+αx[t]+αy[t])([t]+[t])
e
x
e
y
ℱ
⟺
e
x
′
αx
e
y
′
αy
In[7]:=
Clear[position]
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""