SamplePublisher`GrassmannCalculus`
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Examples
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Basic Examples
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In[1]:=
<<GrassmannCalculus`
GrassmannCalculus style icons are used extensively in symbolic factoring Associations. In the following they contain the symbolic expressions associated with each of the GradeBasis elements.
In[2]:=
 | ★ℬ |
4
| SymbolicFactoringAssociation |
Out[2]=
Dimension4,Basis{,,,},Grade2,Symbolc,⋀
,⋀
,⋀
,⋀
,⋀
,⋀
e
1
e
2
e
3
e
4
e
1
e
2
4-space |
e 1 e 2 |
Symbolics |
e
1
e
3
4-space |
e 1 e 3 |
Symbolics |
e
1
e
4
4-space |
e 1 e 4 |
Symbolics |
e
2
e
3
4-space |
e 2 e 3 |
Symbolics |
e
2
e
4
4-space |
e 2 e 4 |
Symbolics |
e
3
e
4
4-space |
e 3 e 4 |
Symbolics |
The following extracts one of them, which must then be unpacked.
In[3]:=
step1[⋀]
[%]
e
1
e
2
 | UnpackIcon |
Out[3]=
4-space |
e 1 e 2 |
Symbolics |
Out[3]=
SymbolicMProduct(++)⋀(++),SymbolicMVector⋀+⋀+⋀-⋀-⋀+(-+)⋀,SymbolicCoefficients{,,,-,-,(-+)},SymbolicVariables{,,,,},EquationFunction(Thread[{,,,-,-,(-+)}##1]&)
c
0,0
e
1
e
3
c
1,3
e
4
c
1,4
e
2
e
3
c
2,3
e
4
c
2,4
c
0,0
e
1
e
2
c
0,0
c
2,3
e
1
e
3
c
0,0
c
2,4
e
1
e
4
c
0,0
c
1,3
e
2
e
3
c
0,0
c
1,4
e
2
e
4
c
0,0
c
1,4
c
2,3
c
1,3
c
2,4
e
3
e
4
c
0,0
c
0,0
c
2,3
c
0,0
c
2,4
c
0,0
c
1,3
c
0,0
c
1,4
c
0,0
c
1,4
c
2,3
c
1,3
c
2,4
c
0,0
c
1,3
c
1,4
c
2,3
c
2,4
c
0,0
c
0,0
c
2,3
c
0,0
c
2,4
c
0,0
c
1,3
c
0,0
c
1,4
c
0,0
c
1,4
c
2,3
c
1,3
c
2,4
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