7.5. Components and derivatives

ComponentValue also works with derivatives of tensors (but not for more general expressions, you can use Coba as a placeholder and then substitute the expression). Remember that with our definitions the components of the derivative are not the derivatives of the components.

In[357]:=

PD[{2, -cartesian}][v[{1, cartesian}]]

Out[357]=

∂_2^ v_ ^1

In[358]:=

ComponentValue[%]

Added independent rule ∂_2^ v_ ^1→∂_2^ v_ ^1 for tensor v

Out[358]=

∂_2^ v_ ^1→∂_2^ v_ ^1

In[359]:=

PD[{1, -polar}][PDpolar[{2, -cartesian}][v[{1, cartesian}]]]

Out[359]=

∂_1^ _2^ v_ ^1

In[360]:=

ComponentValue[%]

Added independent rule ∂_1^ _2^ v_ ^1→∂_1^ _2^ v_ ^1 for tensor v

Out[360]=

∂_1^ _2^ v_ ^1→∂_1^ _2^ v_ ^1

Derivatives are represented by  additional central arguments in ValID:

In[361]:=

TensorValIDs[v]//ColumnForm

Out[361]=

ValID[v,PDpolar[-cartesian],PD[-polar],{{cartesian,-cartesian,-polar}}]
ValID[v,PD[-cartesian],{{cartesian,-cartesian}}]

In[362]:=

DeleteTensorValues[v]

Deleted values for tensor v, derivatives  {PDpolar[-cartesian], PD[-polar]}  and bases  {{cartesian, -cartesian, -polar}}  .

Deleted values for tensor v, derivatives  {PD[-cartesian]}  and bases  {{cartesian, -cartesian}}  .


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