SamplePublisher`GrassmannCalculus`
ExteriorDerivative  |
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Details and Options
Examples
(2)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateVectorSpace |
The exterior derivative the the coordinates are the form basis vectors.
In[3]:=
| ExteriorDerivative |
| GrassmannCoordinates |
| EvaluateExteriorDerivatives |
Out[3]=
{d[x],d[y],d[z]}
Out[3]=
{dx,dy,dz}
An exterior product operating on a function.
In[4]:=
d
[3x2
y
| EvaluateExteriorDerivatives |
Out[4]=
d[3xSin[z]]
2
y
Out[4]=
3(dzxCos[z]+2dyxySin[z]+dxSin[z])
2
y
2
y
Exterior derivatives can be linearly expanded before evaluation
In[5]:=
d
[ax+3y2
z
| ExpandExteriorDerivatives |
| EvaluateExteriorDerivatives |
Out[5]=
d[ax+dxz+3y]
2
z
Out[5]=
ad[x]+d[dxz]+3d[y]
2
z
Out[5]=
adx+6dzyz+3dy-dx⋀dz
2
z
Axioms for the exterior derivative
(1)
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