SamplePublisher`GrassmannCalculus`
MakeSFAExpressionsIcon  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Establish a space.
In[2]:=
 | ★ℬ |
4
Suppose that we had an SFA file for 4-space. As first constructed the grade Associations contain only the expression data for the first element.
GradeBasis
In[3]:=
| SFA |
| UnpackIcon |
SFA[ 4 ] Data |
 | IconExtract |
 | SFA |
Out[3]=
Dimension4,Basis{,,,},Symbolc,2
,3
e
1
e
2
e
3
e
4
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Out[3]=
⋀
e
1
e
2
|
Suppose we wish to add the GradeBasis element ⋀ with its expression Association to this structure. We can create this structure by permuting the variables in the existing ⋀ expression Association.
e
1
e
3
e
1
e
2
In[4]:=
newAssociation=
⋀,
[4],{2,⋀}
| SFAGradeBasisPermute |
e
1
e
3
 | IconExtract |
 | SFA |
e
1
e
2
Out[4]=
SymbolicMProduct(++)⋀(++),SymbolicMVector⋀+⋀+⋀+⋀+(-+)⋀-⋀,SymbolicCoefficients{,,,,(-+),-},SymbolicVariables{,,,,},EquationFunction(Thread[{,,,,(-+),-}##1]&)
c
0,0
e
1
e
2
c
1,2
e
4
c
1,4
e
3
e
2
c
2,2
e
4
c
2,4
c
0,0
c
2,2
e
1
e
2
c
0,0
e
1
e
3
c
0,0
c
2,4
e
1
e
4
c
0,0
c
1,2
e
2
e
3
c
0,0
c
1,4
c
2,2
c
1,2
c
2,4
e
2
e
4
c
0,0
c
1,4
e
3
e
4
c
0,0
c
2,2
c
0,0
c
0,0
c
2,4
c
0,0
c
1,2
c
0,0
c
1,4
c
2,2
c
1,2
c
2,4
c
0,0
c
1,4
c
0,0
c
1,2
c
1,4
c
2,2
c
2,4
c
0,0
c
2,2
c
0,0
c
0,0
c
2,4
c
0,0
c
1,2
c
0,0
c
1,4
c
2,2
c
1,2
c
2,4
c
0,0
c
1,4
In[5]:=
newRule=⋀
[⋀,newAssociation]
e
1
e
3
| MakeSFAExpressionsIcon |
e
1
e
3
Out[5]=
e
1
e
3
|
We then Append this to the grade 2 information, upgrade the grade2 icon and Append it to the data.
SFA[4]
In[6]:=
grade2=Append
[4],{2},newRulegrade2Icon=
[2,grade2]
[4]=Append
[4],2grade2Icon
| IconExtract |
| SFA |
| MakeSFAGradeIcon |
| SFA |
| SFA |
Out[6]=
⋀
,⋀
e
1
e
2
|
e
1
e
3
|
Out[6]=
|
Out[6]=
Dimension4,Basis{,,,},Symbolc,3
,2
e
1
e
2
e
3
e
4
|
|
We can then extract information associated with the GradeBasis ⋀ element.
e
1
e
3
In[7]:=
| IconExtract |
| SFA |
e
1
e
3
Out[7]=
c
0,0
e
1
e
2
c
1,2
e
4
c
1,4
e
3
e
2
c
2,2
e
4
c
2,4
""