SamplePublisher`GrassmannCalculus`
VectorOperator  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Work in the GrassmannPlane.
In[2]:=
 | SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
| ★★S |
A vector operator may be entered by using the long name or the template from the ∇ tab of the Common Operations palette.
In[3]:=
[-3],∂[-3]
 | VectorOperator |
e
x
e
y
e
x
e
y
Out[3]=
{d[-3],d[-3]}
e
x
e
y
e
x
e
y
A vector operator evaluates on all Grassmann expressions but not on non-Grassmann expressions.
In[4]:=
∂[-3]/@qqq,3,xCos[y],★+3+xy⋀//Column
e
x
e
y
2
y
e
x
e
x
e
y
Out[4]=
d[ e x e y |
0 |
2 y 2 y |
-3x e x e y e x e y |
A DirectionalDerivative is just a restricted to scalar functions.
VectorOperator
In[5]:=
[2+3,★+x+y],∂[2+3][y]%//Through
∇
e
x
e
y
e
x
e
y
e
x
e
y
2
x
Out[5]=
[2+3,★+x+y],d[2+3][y]
∇
e
x
e
y
e
x
e
y
e
x
e
y
2
x
Out[5]=
{3+4xy,3+4xy}
2
x
2
x
The following is another way to implement a vector operator:
In[6]:=
(2+3)[]%//Operate
,#&
e
x
e
y
2
x
3
y
 | VectorOperator |
Out[6]=
(2+3)[]
e
x
e
y
2
x
3
y
Out[6]=
9+4x
2
x
2
y
3
y
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