SamplePublisher`GrassmannCalculus`
MathematicaSolveGrassmannEquation  |
|
| | ||||
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Create a 3 dimensional set of linear equations.
In[2]:=
 | SetCoordinateVectorSpace |
In[3]:=
step1=
[{{-1,3,2},{10,-23,-14},{-4,10,6}},{a,b,c}]
 | ComposeGrassmannLinearEquation |
Out[3]=
x(-+10-4)+z(2-14+6)+y(3-23+10)a+b+c
e
x
e
y
e
z
e
x
e
y
e
z
e
x
e
y
e
z
e
x
e
y
e
z
We can extract the matrix and right hand side vector with:
In[4]:=
{matrix,rhs}=%//
| ToGrassmannEquationMatrixForm |
Out[4]=
{{{-1,3,2},{10,-23,-14},{-4,10,6}},{a,b,c}}
This can be written as a conventional matrix equation as follows.
In[5]:=
MatrixForm@matrix.MatrixForm@
MatrixForm@rhs
 | GrassmannCoordinates |
Out[5]=
-1 | 3 | 2 |
10 | -23 | -14 |
-4 | 10 | 6 |
x |
y |
z |
a |
b |
c |
Or generate conventional Mathematica equations and solve them:
In[6]:=
matrix.
rhs//ThreadSolve[%,{x,y,z}]〚1〛
| GrassmannCoordinates |
Out[6]=
{-x+3y+2za,10x-23y-14zb,-4x+10y+6zc}
Out[6]=
xa+b+2c,y-2a+b+3c,z(8a-2b-7c)
1
2
We can also employ regular Mathematica methods directly using:
In[7]:=
| MathematicaSolveGrassmannEquation |
Out[7]=
xa+b+2c,y-2a+b+3c,z(8a-2b-7c)
1
2
 |
|
""