GrassmannCalculus`
ExteriorQuotient  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateBoundVectorSpace |
The following generates the parametrization of a line in 3-space.
In[3]:=
point1=★+3+4+;direction1=5-;line1=point1⋀direction1line1P=
[line1/direction1]
e
x
e
y
e
z
e
x
e
y
 | ExteriorQuotient |
Out[3]=
(★+3+4+)⋀(5-)
e
x
e
y
e
z
e
x
e
y
Out[3]=
★+3+4++(5-)
e
x
e
y
e
z
e
x
e
y
★t
1
We can check that the parametrized line is in the space.
In[4]:=
| ZeroQ |
Out[4]=
True
The following parametrizes a 2-plane attached to a 2-plane.
In[5]:=
| SetCoordinateBoundVectorSpace |
In[6]:=
step1=(★++2)⋀⋀⋀;step2=step1/step1〚{3,4}〛
[step2]
e
u
e
v
e
x
e
y
e
z
| ExteriorQuotient |
Out[6]=
(★++2)⋀⋀⋀
e
u
e
v
e
x
e
y
e
z
e
y
e
z
Out[6]=
(★++2++)⋀(++)
e
u
e
v
e
y
★t
1
e
z
★t
2
e
x
e
y
★t
3
e
z
★t
4
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""