SamplePublisher`GrassmannCalculus`
ToGrassmannEquationForm  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Create a 2 dimensional set of linear equations.
In[2]:=
 | SetCoordinateVectorSpace |
In[3]:=
step1=
[{{1,2},{3,4}},{a,b}]
 | ComposeGrassmannLinearEquation |
Out[3]=
x(+3)+y(2+4)a+b
e
x
e
y
e
x
e
y
e
x
e
y
The equation is initially created in coordinate form where the left hand side is collected on the coordinates. The following converts to equation form where the left hand side is collected on the basis.
In[4]:=
step2=
[step1]
| ToGrassmannEquationForm |
Out[4]=
(x+2y)+(3x+4y)a+b
e
x
e
y
e
x
e
y
Using Gaussian reduction the equation is solved by:
In[5]:=
| PivotGrassmannLinearEquation |
e
x
| PivotGrassmannLinearEquation |
e
y
 | ExtractGrassmannEquation |
e
x
e
y
Out[5]=
(x+2y)-2ya+(-3a+b)
e
x
e
y
e
x
e
y
Out[5]=
x+y(-2a+b)+-
e
x
e
y
e
x
3a
2
b
2
e
y
Out[5]=
x-2a+b,y-
3a
2
b
2
Check by substituting in the original equation.
In[6]:=
step1/.(Rule@@@step3)//Simplify
Out[6]=
True
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