GrassmannCalculus`
ExpandCliffordProducts  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here we evaluate a Clifford product in steps starting with .
ExpandCliffordProducts
In[2]:=
 | ★P |
e
1
e
2
e
1
e
3
e
2
e
3
e
1
e
2
e
3
| ExpandCliffordProducts |
| SimplifyCliffordProducts |
 | 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⋀⋀
e
1
e
2
e
3
e
1
e
2
e
3
e
1
e
2
e
3
e
1
e
2
e
3
Here only the Clifford product is expanded.
In[3]:=
(x+y⋄(p+q))⋁(u+v⋀(w+z))
[%]
 | ExpandCliffordProducts |
 | ★★P |
Out[3]=
(x+y⋄(p+q))⋁(u+v⋀(w+z))
Out[3]=
(x+y⋄p+y⋄q)⋁(u+v⋀(w+z))
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""