GrassmannCalculus`
ExpandGeneralizedProducts  |
|
| | ||||
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here we evaluate a generalize product in steps starting with . In this example it is the same as an interior product.
ExpandGeneralizedProducts
In[2]:=
 | ★P |
e
1
e
2
e
1
e
3
e
2
e
3
 | △ |
1
e
1
e
2
e
3
| ExpandGeneralizedProducts |
| SimplifyGeneralizedProducts |
 | ToMetricElements |
Out[2]=
(a⋀+b⋀+c⋀)(d+e+f)
e
1
e
2
e
1
e
3
e
2
e
3
△
1
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
△
1
e
1
e
1
e
2
△
1
e
2
e
1
e
2
△
1
e
3
e
1
e
3
△
1
e
1
e
1
e
3
△
1
e
2
e
1
e
3
△
1
e
3
e
2
e
3
△
1
e
1
e
2
e
3
△
1
e
2
e
2
e
3
△
1
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)
e
1
e
2
e
3
Here only the generalized Grassmann product is expanded.
In[3]:=
★A;(x+y⋄(p+q))
(u+v⋀(w+z))
[%]
| △ |
λ
| ExpandGeneralizedProducts |
 | ★★P |
Out[3]=
(x+y⋄(p+q))(u+v⋀(w+z))
△
λ
Out[3]=
xu+x(v⋀(w+z))+(y⋄(p+q))u+(y⋄(p+q))(v⋀(w+z))
△
λ
△
λ
△
λ
△
λ
 |
|
 |
|
""