GrassmannCalculus`
ExpandHypercomplexProducts  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here we evaluate a hypercomplex product in steps starting with .
ExpandHypercomplexProducts
In[2]:=
 | ★P |
e
1
e
2
e
1
e
3
e
2
e
3
e
1
e
2
e
3
| ExpandHypercomplexProducts |
| SimplifyHypercomplexProducts |
 | ToMetricElements |
Out[2]=
(a⋀+b⋀+c⋀)∘(d+e+f)
e
1
e
2
e
1
e
3
e
2
e
3
e
1
e
2
e
3
Out[2]=
(a⋀)∘(d)+(a⋀)∘(e)+(a⋀)∘(f)+(b⋀)∘(d)+(b⋀)∘(e)+(b⋀)∘(f)+(c⋀)∘(d)+(c⋀)∘(e)+(c⋀)∘(f)
e
1
e
2
e
1
e
1
e
2
e
2
e
1
e
2
e
3
e
1
e
3
e
1
e
1
e
3
e
2
e
1
e
3
e
3
e
2
e
3
e
1
e
2
e
3
e
2
e
2
e
3
e
3
Out[2]=
ad(⋀)∘+ae(⋀)∘+af(⋀)∘+bd(⋀)∘+be(⋀)∘+bf(⋀)∘+cd(⋀)∘+ce(⋀)∘+cf(⋀)∘
e
1
e
2
e
1
e
1
e
2
e
2
e
1
e
2
e
3
e
1
e
3
e
1
e
1
e
3
e
2
e
1
e
3
e
3
e
2
e
3
e
1
e
2
e
3
e
2
e
2
e
3
e
3
Out[2]=
-ae-bf+ad-cf+bd+ce+cd⋀⋀-be⋀⋀+af⋀⋀
2,1,1
★σ
2,1,1
★σ
e
1
2,1,1
★σ
2,1,1
★σ
e
2
2,1,1
★σ
2,1,1
★σ
e
3
2,0,1
★σ
e
1
e
2
e
3
2,0,1
★σ
e
1
e
2
e
3
2,0,1
★σ
e
1
e
2
e
3
Here only the hypercomplex product is expanded.
In[3]:=
(x+y⋄(p+q))∘(u+v⋀(w+z))
[%]
 | ExpandHypercomplexProducts |
 | ★★P |
Out[3]=
(x+y⋄(p+q))∘(u+v⋀(w+z))
Out[3]=
x∘u+x∘(v⋀(w+z))+(y⋄(p+q))∘u+(y⋄(p+q))∘(v⋀(w+z))
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