GrassmannCalculus`
ConvertGeneralizedToInterior  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
★A;
;
 | ★ℬ |
4
 | ★P |
The generalized product is the pathway to the customary expression in terms of exterior and interior products.
In[3]:=
p⋄q%//
%//
| ConvertCliffordToGeneralized |
| ConvertGeneralizedToInterior |
Out[3]=
p⋄q
Out[3]=
pq+pq
△
0
△
1
Out[3]=
p⊖q+p⋀q
In[4]:=
Tablep
q,{i,0,2}%//
Grade[%]
 | △ |
i
| ConvertGeneralizedToInterior |
Out[4]=
pq,pq,pq
△
0
△
1
△
2
Out[4]=
{p⋀q,p⊖q,0}
Out[4]=
{2,0,★0}
The following show the conversions and grades for several graded expressions. The grades decrease by 2 as the order of the generalized product increases by 1.
In[5]:=
★A;
;Table
,{i,0,3}step1=%//
//ColumnGrade[step1]
| ★ℬ |
6
α
3
| △ |
i
β
2
| ConvertGeneralizedToInterior |
Out[5]=
,,,
α
3
△
0
β
2
α
3
△
1
β
2
α
3
△
2
β
2
α
3
△
3
β
2
Out[5]=
α 3 β 2 |
( α 3 β 2 β 3 α 3 β 3 β 2 |
α 3 β 2 |
0 |
Out[5]=
{5,3,1,★0}
In[6]:=
★A;
;Table
,{i,0,3}step1=%//
//ColumnGrade[step1]
| ★ℬ |
6
α
3
| △ |
i
β
3
| ConvertGeneralizedToInterior |
Out[6]=
,,,
α
3
△
0
β
3
α
3
△
1
β
3
α
3
△
2
β
3
α
3
△
3
β
3
Out[6]=
α 3 β 3 |
( α 3 β 4 β 5 β 6 α 3 β 5 β 4 β 6 α 3 β 6 β 4 β 5 |
( α 3 β 4 β 5 β 6 α 3 β 4 β 6 β 5 α 3 β 5 β 6 β 4 |
α 3 β 3 |
Out[6]=
{6,4,2,0}
In[7]:=
| ★★P |
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