SamplePublisher`GrassmannCalculus`DifferentialGeometry`
LeibnizDirectionalDerivatives  |
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Details and Options
Examples
(1)
Basic Examples
(1)
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<<GrassmannCalculus`
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savePreferences=
;
 | AllPreferences |
Work in the GrassmannPlane.
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SetPreferences["GrassmannPlane","Vector"]
[];
[f[__],g[__]];
| ★★V |
| ★★S |
The Leibnizian breakout of derivatives is done automatically by Mathematica but here it can also be done explicitly on expressions with arguments.
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 | DefineScalarFunction |
| DefineScalarFunction |
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∇
e
x
| LeibnizDirectionalDerivatives |
| InsertPosition |
| EvaluateDirectionalDerivatives |
Out[5]=
∇
e
x
Out[5]=
f2[][]f1[]+f1[][]f2[]
∇
e
x
∇
e
x
Out[5]=
(x+y)[](xy)+xy[](x+y)
∇
e
x
∇
e
x
Out[5]=
xy+y(x+y)
The following is a generic version. The and expressions were declared as scalars above.
f
g
In[6]:=
∇
e
x
| LeibnizDirectionalDerivatives |
| EvaluateDirectionalDerivatives |
Out[6]=
∇
e
x
Out[6]=
g[][]f[]+f[][]g[]
∇
e
x
∇
e
x
Out[6]=
g[x,y][]f[x,y]+f[x,y][]g[x,y]
∇
e
x
∇
e
x
Out[6]=
g[x,y][x,y]+f[x,y][x,y]
(1,0)
f
(1,0)
g
In[7]:=
ClearAll[f1,f2]
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| RestorePreferences |
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