GrassmannCalculus`
ComposeGradedForm  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Establish the default book space.
In[2]:=
★A;
Suppose that you wish to explore the general form that the interior product of two general Grassmann numbers in a 3-space takes. We enter the product using multi-graded symbols:
In[3]:=
X=⊖;
x
{0,1,2,3}
y
{0,1,2,3}
We can apply to convert this from its multigraded form to its graded form:
ComposeGradedForm
In[4]:=
X1=
[X]
 | ComposeGradedForm |
Out[4]=
(+++)⊖+++
x
0
x
1
x
2
x
3
y
0
y
1
y
2
y
3
This graded form now allows us to expand and simplify terms:
In[5]:=
 | ★ |
Out[5]=
x
1
y
1
x
2
y
1
x
2
y
2
x
3
y
1
x
3
y
2
x
3
y
3
x
0
y
0
x
1
y
0
x
2
y
0
x
3
y
0
ComposeGradedForm
In[6]:=
| ComposeGradedForm |
 | |
{0,2}
| |
{1,3}
 | |
{1,2}
Out[6]=
((+)⋀(+))⋄(+)
0
2
1
3
1
2
ComposeGradedForm
In[7]:=
M=Table
,{2},{2}//MatrixForm
| |
{1,2,3}
Out[7]//MatrixForm=
{1,2,3} | {1,2,3} |
{1,2,3} | {1,2,3} |
In[8]:=
| ComposeGradedForm |
Out[8]//MatrixForm=
1 2 3 | 1 2 3 |
1 2 3 | 1 2 3 |
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