SamplePublisher`GrassmannCalculus`
SFA  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Create an SFA Association for grade 2 in a 3-dimensional space.
In[2]:=
 | ★ℬ |
3
 | ComputeNSpaceFactoringData |
Out[2]=
SFA[ 3 ] Data |
Create an initialization to place in a notebook by copying and pasting the icon into the following statement.
In[3]:=
 | SFA |
| UnpackIcon |
SFA[ 3 ] Data |
Evaluation give the following structure.
In[4]:=
| SFA |
Out[4]=
Dimension3,Basis{,,},Symbolc,2
e
1
e
2
e
3
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Information at the various levels can be obtained with . Give the list of keys to the level desired. Here we obtain the symbolic expressions for the first GradeBasis element in grade 2.
SFAExtract
In[5]:=
expressionAssoc=
[{2,⋀}]
| SFAExtract |
e
1
e
2
Out[5]=
SymbolicMProduct(+)⋀(+),SymbolicMVector⋀+⋀-⋀,SymbolicCoefficients{,,-},SymbolicVariables{,,},EquationFunction(Thread[{,,-}##1]&)
c
0,0
e
1
e
3
c
1,3
e
2
e
3
c
2,3
c
0,0
e
1
e
2
c
0,0
c
2,3
e
1
e
3
c
0,0
c
1,3
e
2
e
3
c
0,0
c
0,0
c
2,3
c
0,0
c
1,3
c
0,0
c
1,3
c
2,3
c
0,0
c
0,0
c
2,3
c
0,0
c
1,3
The keys above can be pasted from the launched by:
SFAKeysPalette
In[6]:=
| SFAKeysPalette |
A specific 2-vector with symbolic coefficients might be:
In[7]:=
expressionAssoc["SymbolicMVector"]/.Thread[expressionAssoc["SymbolicCoefficients"]{a,b,c}]
Out[7]=
a⋀+b⋀+c⋀
e
1
e
2
e
1
e
3
e
2
e
3
We substitute these coefficients in the equation function and solve to obtain a factored form.
In[8]:=
equations=expressionAssoc["EquationFunction"][{a,b,c}]solution=Solve[equations,expressionAssoc["SymbolicVariables"]]expressionAssoc["SymbolicMProduct"]/.solution〚1〛expressionAssoc["SymbolicMVector"]/.solution〚1〛
Out[8]=
{a,b,-c}
c
0,0
c
0,0
c
2,3
c
0,0
c
1,3
Out[8]=
a,-,
c
0,0
c
1,3
c
a
c
2,3
b
a
Out[8]=
a-⋀+
e
1
c
e
3
a
e
2
b
e
3
a
Out[8]=
a⋀+b⋀+c⋀
e
1
e
2
e
1
e
3
e
2
e
3
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""