GrassmannCalculus`
ToInteriorProducts  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here are the Clifford and hypercomplex products of two 1-elements in 3-space converted to exterior and interior products. In this case the resulting interior product is a scalar product.
In[2]:=
★A;
[{x⋄y,x∘y}]
 | ToInteriorProducts |
Out[2]=
x⊖y+x⋀y,(x⊖y)+x⋀y
1,1,1
★σ
1,0,1
★σ
Here is the Clifford product of two 2-elements in a 4-space converted to exterior and interior products. Note that the has been automatically converted to the simple exterior product ⋀ wherever it was necessary for further expansion of an intermediate generalized Grassmann product into interior product form. Hence the expression is valid only for simple .
y
2
y
2
y
3
y
2
In[3]:=
| ★ℬ |
4
| ToInteriorProducts |
x
2
y
2
Out[3]=
-⊖-(⊖)⋀+(⊖)⋀+⋀
x
2
y
2
x
2
y
2
y
3
x
2
y
3
y
2
x
2
y
2
In the case is not simple, it should be expressed in a non-simple form. In a 4-space for example, we can do this by writing:
y
2
In[4]:=
Y=
⋄+
| ★ℰ |
x
2
y
2
z
2
Out[4]=
x
2
y
2
x
2
z
2
In[5]:=
| ★ℬ |
4
| ToInteriorProducts |
Out[5]=
-⊖-⊖-(⊖)⋀+(⊖)⋀-(⊖)⋀+(⊖)⋀+⋀+⋀
x
2
y
2
x
2
z
2
x
2
y
2
y
3
x
2
y
3
y
2
x
2
z
2
z
3
x
2
z
3
z
2
x
2
y
2
x
2
z
2
Here is the conversion to interior products in a 5-space of a multigraded Clifford product involving the simple factor .
y
2
In[6]:=
| ★ℬ |
5
| ToInteriorProducts |
x
{0,1,2,3}
y
2
Out[6]=
-⊖-⊖+⊖+-(⊖)⋀+(⊖)⋀-⋀⊖+⋀⊖+⋀+⋀+⋀
x
2
y
2
x
3
y
2
y
2
x
1
x
0
y
2
x
2
y
2
y
3
x
2
y
3
y
2
y
2
x
3
y
3
y
3
x
3
y
2
x
1
y
2
x
2
y
2
x
3
y
2
In[7]:=
Clear[Y]
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