GrassmannCalculus`
OrderExterior  |
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Details and Options
Examples
(2)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
★A;
;
 | ★ℬ |
5
The following orders two exterior products in basis elements.
In[3]:=
{⋀⋀⋀,⋀⋀⋀}
/@%
e
2
e
1
e
4
e
3
e
2
e
1
e
3
e
4
 | OrderExterior |
Out[3]=
{⋀⋀⋀,⋀⋀⋀}
e
2
e
1
e
4
e
3
e
2
e
1
e
3
e
4
Out[3]=
{⋀⋀⋀,-(⋀⋀⋀)}
e
1
e
2
e
3
e
4
e
1
e
2
e
3
e
4
The following illustrates the ordering of a number of graded symbol expressions.
1) In the first case the odd grade factors are placed first and the even grade factors last.
2) In the second case the two odd grade factors are interchanged producing a negative sign and the two even grade elements are sorted according to Mathematica Sort.
3) In the third case two multigraded symbols are used. One is manifestly even grade and so goes in the trailing subset of factors. The other is neither even or odd and goes in the leading subset of factors.
1) In the first case the odd grade factors are placed first and the even grade factors last.
2) In the second case the two odd grade factors are interchanged producing a negative sign and the two even grade elements are sorted according to Mathematica Sort.
3) In the third case two multigraded symbols are used. One is manifestly even grade and so goes in the trailing subset of factors. The other is neither even or odd and goes in the leading subset of factors.
In[4]:=
⋀⋀⋀,⋀⋀⋀,⋀⋀⋀
/@%
α
1
α
2
α
3
α
4
α
3
β
2
α
1
α
4
α
1
α
{2,4}
α
{1,2}
α
4
| OrderExterior |
Out[4]=
⋀⋀⋀,⋀⋀⋀,⋀⋀⋀
α
1
α
2
α
3
α
4
α
3
β
2
α
1
α
4
α
1
α
{2,4}
α
{1,2}
α
4
Out[4]=
⋀⋀⋀,-⋀⋀⋀,⋀⋀⋀
α
1
α
3
α
2
α
4
α
1
α
3
α
4
β
2
α
1
α
{1,2}
α
4
α
{2,4}
In the following expression none of the factors are manifestly even grade. The grade of is undetermined; it keeps its place and all other factors are ordered by the .
F
StandardOrderingFunction
In[5]:=
y⋀x⋀(p⋀q⊖y)⋀⋀F⋀
[%]
e
2
e
1
| OrderExterior |
Out[5]=
y⋀x⋀(p⋀q⊖y)⋀⋀F⋀
e
2
e
1
Out[5]=
e
1
e
2
OrderExterior Algorithm
(1)
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