GrassmannCalculus`
OrderRegressive  |
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Details and Options
Examples
(2)
Basic Examples
(1)
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<<GrassmannCalculus`
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★A;
;
 | ★ℬ |
5
The following orders two regressive products in basis elements. Since we are in the complementary grades are all even.
★ℬ
5
In[3]:=
{⋁⋁⋁,⋁⋁⋁}
/@%
e
2
e
1
e
4
e
3
e
2
e
1
e
3
e
4
 | OrderRegressive |
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 complementary grade factors are placed first and the even complementary grade factors last.
2) In the second case the two odd complementary grade factors are interchanged producing a negative sign and the two even complementary grade elements are sorted according to Mathematica Sort.
3) In the third case two multigraded symbols are used. One is manifestly even complementary 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, maintaining its position.
1) In the first case the odd complementary grade factors are placed first and the even complementary grade factors last.
2) In the second case the two odd complementary grade factors are interchanged producing a negative sign and the two even complementary grade elements are sorted according to Mathematica Sort.
3) In the third case two multigraded symbols are used. One is manifestly even complementary 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, maintaining its position.
In[4]:=
⋁⋁⋁,⋁⋁⋁,⋁⋁⋁
/@%
α
1
α
2
α
3
α
4
β
3
α
4
α
1
α
2
α
1
α
{1,3}
α
{1,2}
α
4
| OrderRegressive |
Out[4]=
⋁⋁⋁,⋁⋁⋁,⋁⋁⋁
α
1
α
2
α
3
α
4
β
3
α
4
α
1
α
2
α
1
α
{1,3}
α
{1,2}
α
4
Out[4]=
⋁⋁⋁,-⋁⋁⋁,⋁⋁⋁
α
2
α
4
α
1
α
3
α
2
α
4
α
1
β
3
α
{1,2}
α
4
α
1
α
{1,3}
In the following expression all of the factors, except , are manifestly even complementary grade. is ungraded and is the only member of the leading subset, the other factors are sorted in standard Mathematica order.
F
F
In[5]:=
y⋁x⋁(p⋀q⊖y)⋁⋁F⋁
[%]
e
2
e
1
| OrderRegressive |
Out[5]=
y⋁x⋁(p⋀q⊖y)⋁⋁F⋁
e
2
e
1
Out[5]=
F⋁x⋁y⋁(p⋀q⊖y)⋁⋁
e
1
e
2
OrderRegressive Algorithm
(1)
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