I have several variables (coordinates) $x_1, x_2, x_3, x_4, z$ and a lot (21, to be precise) functions $g_i$ which are assumed to depend on $x_1, x_2,x_3, x_4$, but not on $z$. I also have a function Differentiation which uses Dt in its definition. I would like to apply Differentiation to my functions $g_i$.

I found that this question proposed giving constants the attribute "Constant". However, I cannot apply it directly, as my functions are constants only with respect to one variable.

Is there any way to do this?

  • $\begingroup$ Dt[x^2 y + z, x, y, Constants -> {z}]? $\endgroup$ – kglr Sep 29 '18 at 1:40
  • $\begingroup$ or Internal`InheritedBlock[{Dt}, SetOptions[Dt, Constants -> {z}]; Differentiation[x1,x2,x3,x4,z]]? $\endgroup$ – kglr Sep 29 '18 at 1:46
  • $\begingroup$ Hello, @kglr ! I tried to implement your suggestion with a simple function diff[expr_, x_] := Dt[expr, x];. However, InternalInheritedBlock[{Dt}, SetOptions[Dt, Constants -> {z}]];diff[z r, z]` gives the same answer as diff[r z , z] - r + z Dt[r, z], when expected simply r. Did I somehow misinterpret your suggestion? $\endgroup$ – user108687 Sep 29 '18 at 1:56
  • $\begingroup$ @klgr And as far as I understand, Constant attribute corresponds to setting all derivative of a variable to zero. And I want all the derivatives of other variables wrt this one to be set to zero. $\endgroup$ – user108687 Sep 29 '18 at 2:04
  • $\begingroup$ @klgr I think that I've found solution: ff[expr_, x_] = Dt[expr, x]; A /: Dt[A, z] = 0; ff[A B, z] returns A Dt[B, z]. Thanks for help! $\endgroup$ – user108687 Sep 29 '18 at 2:13

With suggestions from @kglr I arrived at the following solution for a toy problem of differentiating $AB$ with respect to $z$, assuming that $A$ doesn't depend on $z$, using A /: Dt[A, z] = 0, which sets the derivative of $A$ with respect to $z$ equal to zero:

ff[expr_, x_] = Dt[expr, x];
A /: Dt[A, z] = 0;
ff[A B, z]

returns A Dt[B, z].

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