GrassmannCalculus`
ToRegressiveProducts  |
|
| | ||||
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here is the conversion of some different Grassmann products in 3-space to expressions involving regressive products and complements.
In[2]:=
 | ToRegressiveProducts |
x
j
y
k
Out[2]=
x
j
y
k
In[3]:=
| ToRegressiveProducts |
x
j
y
k
Out[3]=
x
j
y
k
In[4]:=
| ToRegressiveProducts |
x
3
 | △ |
1
y
2
Out[4]=
-⋁⋁+⋁⋁
y
2
x
3
y
3
y
3
x
3
y
2
In[5]:=
| ToRegressiveProducts |
x
3
y
2
Out[5]=
-⋁⋁+⋁⋁-⋁
y
2
x
3
y
3
y
3
x
3
y
2
x
3
y
2
Here is an expression for the Clifford product of two Grassmann numbers in a 3-space leading to a somewhat more complex conversion.
In[6]:=
★A;X=⋄;
h
{0,1,2,3}
k
{0,1,2,3}
You can express this product in terms of only regressive products and complement operations by applying .
ToExteriorProducts
In[7]:=
X1=
[X]
| ToRegressiveProducts |
Out[7]=
h
2
k
3
h
3
h
3
k
3
h
2
k
2
h
3
k
3
k
3
h
3
k
2
h
1
k
1
h
1
k
2
k
1
h
2
h
2
k
2
k
3
h
2
k
3
k
2
h
3
k
4
k
5
k
6
h
3
k
4
k
6
k
5
h
3
k
5
k
6
k
4
h
0
k
0
h
1
k
0
h
2
k
0
h
3
k
0
h
0
k
1
h
0
k
2
h
0
k
3
h
1
k
1
h
2
k
1
h
2
k
2
h
3
k
1
h
3
k
2
h
3
k
3
k
2
h
1
k
3
h
1
k
3
h
2
Applying reduces some of the complement overburden.
GrassmannSimplify
In[8]:=
| ★ |
Out[8]=
h
1
k
1
h
2
k
1
h
2
k
2
h
3
k
1
h
3
k
2
h
3
k
3
k
2
h
1
k
3
h
1
k
3
h
2
h
0
k
0
h
1
k
0
h
2
k
0
h
3
k
0
h
0
k
1
h
0
k
2
h
0
k
3
h
2
k
2
k
3
h
2
k
3
k
2
h
3
k
4
k
5
k
6
h
3
k
4
k
6
k
5
h
3
k
5
k
6
k
4
h
2
k
3
h
3
h
3
k
3
h
2
k
2
h
3
k
3
k
3
h
3
k
2
h
1
k
1
h
1
k
2
k
1
h
2
In[9]:=
Clear[X,X1]
 |
|
""