SamplePublisher`GrassmannCalculus`
EvaluateCrossProducts  |
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Details and Options
Examples
(10)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
★A;
In 3-space the following is the regular cross product.
In[3]:=
e
1
G
e
2
 | EvaluateCrossProducts |
Out[3]=
e
1
G
e
2
Out[3]=
e
3
Symbolic vectors evaluate to the Grassmann algebra definition of CrossProduct.
In[4]:=
pq
[%]
G
| EvaluateCrossProducts |
Out[4]=
pq
G
Out[4]=
p⋀q
A scalar argument acts as a weighted .
GrassmannComplement
In[5]:=
ap
[%]
G
| EvaluateCrossProducts |
Out[5]=
(a)p
G
Out[5]=
a
p
Nested cross products are evaluated as follows:
In[6]:=
pqr
[%]
G
G
| EvaluateCrossProducts |
Out[6]=
pqr
G
G
Out[6]=
p⋀q⊖r
Further simplification can either be performed in extra steps or by specifying additional steps in the second argument of .
EvaluateCrossProducts
In[7]:=
pqr
%,
G
G
| EvaluateCrossProducts |
 | ToInnerProducts |
Out[7]=
pqr
G
G
Out[7]=
q(p⊖r)-p(q⊖r)
Properties of the CrossProduct
(8)
Orthogonality
(1)
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