GrassmannCalculus`
ToScalarProducts  |
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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 converted to scalar products.
In[2]:=
★A;
[{x⋄y,x∘y}]
 | ToScalarProducts |
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 3-space converted to scalar products.
In[3]:=
X=
⋄
| ToScalarProducts |
x
2
y
2
Out[3]=
(⊖)(⊖)-(⊖)(⊖)-(⊖)⋀+(⊖)⋀+(⊖)⋀-(⊖)⋀
x
2
y
3
x
3
y
2
x
2
y
2
x
3
y
3
x
3
y
3
x
2
y
2
x
3
y
2
x
2
y
3
x
2
y
3
x
3
y
2
x
2
y
2
x
3
y
3
By reducing expressions to scalar products you could, for example, explore the associativity of the Clifford product in a 3-space.
In[4]:=
| ★ℬ |
3
 | ToScalarProducts |
 | ToScalarProducts |
| ToScalarProducts |
| ToScalarProducts |
Out[4]=
True
In more detail:
In[5]:=
| ★ℬ |
3
 | ToScalarProducts |
| ToScalarProducts |
| ToScalarProducts |
| ToScalarProducts |
Out[5]=
z(x⊖y)-y(x⊖z)+x(y⊖z)+x⋀y⋀z
Out[5]=
z(x⊖y)-y(x⊖z)+x(y⊖z)+x⋀y⋀z
Out[5]=
True
 |
|
""