SamplePublisher`GrassmannCalculus`
DefineCoordinateElements  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateVectorSpace |
Compose a 3-dimensional Grassmann linear equation.
In[3]:=
GE=
[{{0,2,0},{-6,12,-3},{3,-4,1}},{a,b,c}]
 | ComposeGrassmannLinearEquation |
Out[3]=
y(2+12-4)+z(-3+)+x(-6+3)a+b+c
e
x
e
y
e
z
e
y
e
z
e
y
e
z
e
x
e
y
e
z
The coordinate elements are the coefficients of the coordinates on the left hand side. They have already been defined as functions by the compose statement.
c
In[4]:=
Inactive[c]/@
Activate[%]
| GrassmannCoordinates |
Out[4]=
{c[x],c[y],c[z]}
Out[4]=
{-6+3,2+12-4,-3+}
e
y
e
z
e
x
e
y
e
z
e
y
e
z
If we had edited the equation, or wanted to save the coordinate elements under a different name we could use:
In[5]:=
| DefineCoordinateElements |
| GrassmannCoordinates |
Out[5]=
(-6+3)⋀(2+12-4)⋀(-3+)
e
y
e
z
e
x
e
y
e
z
e
y
e
z
Out[5]=
{d[x],d[y],d[z]}
Out[5]=
{-6+3,2+12-4,-3+}
e
y
e
z
e
x
e
y
e
z
e
y
e
z
Performing a Gaussian operation changes the coordinate elements. Here we do a Gaussian pivot and reset the coordinate elements under a d label. We also display the coordinate form of the equation to check that the coordinate elements correspond.
In[6]:=
| PivotGrassmannLinearEquation |
e
x
| ToGrassmannCoordinateForm |
| GrassmannCoordinates |
Out[6]=
y+(-6x-3z)+(3x+z)+(-6a+b)+(2a+c)
e
x
e
y
e
z
a
e
x
2
e
y
e
z
Out[6]=
y+z(-3+)+x(-6+3)+(-6a+b)+(2a+c)
e
x
e
y
e
z
e
y
e
z
a
e
x
2
e
y
e
z
Out[6]=
{d[x],d[y],d[z]}
Out[6]=
{-6+3,,-3+}
e
y
e
z
e
x
e
y
e
z
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