GrassmannCalculus`
ComposeGeneralizedGradedForm  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set a 5-dimensional book vector space and turn on precedence showing.
In[2]:=
 | ★ℬ |
5
 | ★P |
Here only the Generalized product is expanded.
In[3]:=
x
{1,3}
y
{1,3}
p
{2,4}
 | △ |
2
q
{2,4}
| ComposeGeneralizedGradedForm |
Out[3]=
x
{1,3}
y
{1,3}
p
{2,4}
△
2
q
{2,4}
Out[3]=
x
{1,3}
y
{1,3}
p
2
p
4
△
2
q
2
q
4
Here the regressive products are also expanded because they are inside the Generalized product.
In[4]:=
p
{2,4}
q
{2,4}
| △ |
2
x
{1,3}
y
{1,3}
| ComposeGeneralizedGradedForm |
Out[4]=
⋁⋁
p
{2,4}
q
{2,4}
△
2
x
{1,3}
y
{1,3}
Out[4]=
(+)⋁(+)(+)⋁(+)
p
2
p
4
q
2
q
4
△
2
x
1
x
3
y
1
y
3
Here we change the precedence such that only the central Generalized product is expanded.
In[5]:=
p
{2,4}
q
{2,4}
 | △ |
2
x
{1,3}
y
{1,3}
| ComposeGeneralizedGradedForm |
Out[5]=
p
{2,4}
q
{2,4}
△
2
x
{1,3}
y
{1,3}
Out[5]=
p
{2,4}
q
2
q
4
△
2
x
1
x
3
y
{1,3}
Placeholders may be used instead of symbols. (This appears not to work but works nonselectively with ComposeGradedForm.)
In[6]:=
x
{1,3}
y
{1,3}
| |
{2,4}
| △ |
2
| |
{2,4}
| ComposeInteriorGradedForm |
| ComposeGradedForm |
Out[6]=
x
{1,3}
y
{1,3}
{2,4}
△
2
{2,4}
Out[6]=
x
{1,3}
y
{1,3}
{2,4}
△
2
{2,4}
Out[6]=
(+)⋀(+)+(+)(+)
x
1
x
3
y
1
y
3
2
4
△
2
2
4
In[7]:=
 | ★★P |
 |
|
""