SamplePublisher`GrassmannCalculus`
GenerateCoordinateEquations  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
For a line in 2-space
In[2]:=
 | SetCoordinateBoundVectorSpace |
 | RandomGrassmannPoint |
| RandomGrassmannVector |
| GenerateCoordinateEquations |
Out[2]=
(★+4+)⋀
e
x
e
y
e
x
Out[2]=
{y1}
For a symbolic line:
In[3]:=
| annotate |
(★+a+b)⋀(c+d)
e
x
e
y
e
x
e
y
| annotate |
| GenerateCoordinateEquations |
 | AssociationOutput |
| annotate |
| annotate |
| FastZeroQ |
Out[3]=
A symbolic line.
Out[3]=
(★+a+b)⋀(c+d)
e
x
e
y
e
x
e
y
Out[3]=
Association solution and resulting equation.
Out[3]=
{dx-cy-bc+ad}
Out[3]=
Solution for y in terms of x and a parameterization in terms of x of the points on the line. If c is zero solve for x instead.
Out[3]=
y
bc-ad+dx
c
Out[3]=
★+b-+x+
e
y
ad
e
y
c
e
x
d
e
y
c
Out[3]=
Test if the parametrized points are on the line.
Out[3]=
Points on the line?True
The following generates the equations for a plane in 4-space and uses the Association output.
In[4]:=
| SetCoordinateBoundVectorSpace |
| RandomGrassmannPoint |
| RandomGrassmannVectorElement |
 | FastExteriorExpand |
| GenerateCoordinateEquations |
| AssociationOutput |
| AssociationKeysPalette |
Out[4]=
(★+-2--4)⋀(-298+61-536+6)⋀(-49+10-88+)
e
w
e
x
e
y
e
z
e
w
e
x
e
y
e
z
e
w
e
x
e
y
e
z
Out[4]=
9★⋀⋀-40★⋀⋀-4★⋀⋀-8★⋀⋀+★⋀⋀-8★⋀⋀-97⋀⋀-43⋀⋀+148⋀⋀+49⋀⋀
e
w
e
x
e
w
e
y
e
w
e
z
e
x
e
y
e
x
e
z
e
y
e
z
e
w
e
x
e
y
e
w
e
x
e
z
e
w
e
y
e
z
e
x
e
y
e
z
Out[4]=
{8x+y+8z-49,2w-y+10z-37}
The Association Keys palette can be used to select output from the Association. Use the top button to paste the Association name and then paste one of the Keys from the lower drop down menu. For example to retrieve the Coordinate Probe (a position vector) use
In[5]:=
case2s4["Coordinate Probe"]
Out[5]=
★+w+x+y+z
e
w
e
x
e
y
e
z
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""