SamplePublisher`GrassmannCalculus`
GrassmannLinearSolve  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateVectorSpace |
In[3]:=
GE=
[{{9,2,-3},{0,1,-3},{3,1,-3}},{a,b,c}]solveFunction=
[GE];
 | ComposeGrassmannLinearEquation |
 | GrassmannLinearSolve |
Out[3]=
z(-3-3-3)+y(2++)+x(9+3)a+b+c
e
x
e
y
e
z
e
x
e
y
e
z
e
x
e
z
e
x
e
y
e
z
The solveFunction can be applied to a right hand side.
In[4]:=
rhs={a,b,c}.Basis//ThreadsolveSolutions=solveFunction[rhs]GE/.solveSolutions//Simplify
Out[4]=
a+b+c
e
x
e
y
e
z
Out[4]=
x(-b+c),ya+2b-3c,z(a+b-3c)
1
3
1
3
Out[4]=
True
Or a different right hand side.
In[5]:=
rhs={1,-2,3}.BasissolveFunction[rhs]GE〚1〛rhs/.%//Simplify
Out[5]=
e
x
e
y
e
z
Out[5]=
x,y-12,z-
5
3
10
3
Out[5]=
True
We can see that this is the inverse Function by applying it to the columns of the original equation.
In[6]:=
step1=Table
,{3}step2=solveFunction/@c
MapThread[#1/.#2&,{step1,step2}]//MatrixForm
| GrassmannCoordinates |
| GrassmannCoordinates |
Out[6]=
{{x,y,z},{x,y,z},{x,y,z}}
Out[6]=
{{x1,y0,z0},{x0,y1,z0},{x0,y0,z1}}
Out[6]//MatrixForm=
1 | 0 | 0 |
0 | 1 | 0 |
0 | 0 | 1 |
 |
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