SamplePublisher`GrassmannCalculus`
PivotGrassmannLinearEquation  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateVectorSpace |
Compose a Grassmann linear equation in equation form.
In[3]:=
GEE=
[{{-26,16,-8},{4,-4,1},{-10,6,-3}},{a,b,c}]//
 | ComposeGrassmannLinearEquation |
 | ToGrassmannEquationForm |
Out[3]=
(-26x+16y-8z)+(4x-4y+z)+(-10x+6y-3z)a+b+c
e
x
e
y
e
z
e
x
e
y
e
z
Pivot on element .
{,x}
e
x
In[4]:=
step1=
[GEE][{,x}]
| PivotGrassmannLinearEquation |
e
x
Out[4]=
x-++--+-+-++b+-+c
8y
13
4z
13
e
x
20y
13
3z
13
e
y
2y
13
z
13
e
z
a
e
x
26
2a
13
e
y
5a
13
e
z
Pivot on element .
{,y}
e
y
In[5]:=
step2=
[step1][{,y}]
| PivotGrassmannLinearEquation |
e
y
Out[5]=
x++y++--+--+--+c
2z
5
e
x
3z
20
e
y
z
e
z
10
a
10
2b
5
e
x
a
10
13b
20
e
y
2a
5
b
10
e
z
Pivot on element .
{,z}
e
z
In[6]:=
step3=
[step2][{,z}]
| PivotGrassmannLinearEquation |
e
z
Out[6]=
x+y+z-4c+--+(-4a-b+10c)
e
x
e
y
e
z
3a
2
e
x
a
2
b
2
3c
2
e
y
e
z
The equation is now in solved form. We can extract the individual solutions with:
In[7]:=
| ExtractGrassmannEquation |
Out[7]=
x-4c,y--,z-4a-b+10c
3a
2
a
2
b
2
3c
2
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