How to define a variable to be a function of all the arguments but one?

Question

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?

or Internal`InheritedBlock[{Dt}, SetOptions[Dt, Constants -> {z}]; Differentiation[x1,x2,x3,x4,z]]? — kglr, Sep 29 '18 at 01:46
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 asdiff[r z , z]-r + z Dt[r, z], when expected simplyr`. Did I somehow misinterpret your suggestion? — user108687, Sep 29 '18 at 01:56
@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. — user108687, Sep 29 '18 at 02:04
@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! — user108687, Sep 29 '18 at 02:13
that's a very good solution. I suggest you self-answer the question. — kglr, Sep 29 '18 at 02:18
@ΑλέξανδροςΖεγγ could you explain, what MWE is, please? — user108687, Oct 29 '18 at 03:33

score 1 · Answer 1 · answered Sep 29 '18 at 02:30

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].

How to define a variable to be a function of all the arguments but one?

1 Answers1