SamplePublisher`GrassmannCalculus`
CrossProduct  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
★A;
CrossProduct formats on output with a symbol.
G
In[3]:=
 | CrossProduct |
Out[3]=
pq
G
It may be entered via the Common Operations palette as:
In[4]:=
pq
G
Out[4]=
pq
G
Since CrossProduct is a binary operation the regular input form will give a warning on more than two arguments.
In[5]:=
| CrossProduct |
However, the palette allows multiple clicking and automatically nests the products from the left if clicked on the first entry.
In[6]:=
pqrs%//FullForm
G
G
G
Out[6]=
pqrs
G
G
G
Out[6]//FullForm=
CrossProduct[CrossProduct[CrossProduct[p,q],r],s]
If precedence parentheses are used, or if the template is repeatedly clicked on the right argument then it can be nested from the right. This non-standard grouping is then indicated in the display.
In[7]:=
p(q(rs))%//FullForm
G
G
G
Out[7]=
p(q(rs))
G
G
G
Out[7]//FullForm=
CrossProduct[p,CrossProduct[q,CrossProduct[r,s]]]
A cross product of two cross products would be entered as:
In[8]:=
(pq)(rs)%//FullForm
Out[8]=
pq(rs)
G
G
G
Out[8]//FullForm=
CrossProduct[CrossProduct[p,q],CrossProduct[r,s]]
And other combinations of nesting could be used. The arguments do not have to be vectors but could be any Grassmann expression.
In[9]:=
(1+a⋀)⋀
e
1
e
2
e
2
e
3
Out[9]=
(1+a⋀)(⋀)
e
1
e
2
G
e
2
e
3
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""