derivativemaxima

Substituting the derivative of a term into an expression containing higher derivatives

I am trying to substitute the first order derivative of a term into an expression that contains higher order derivatives and am not getting the desired behavior.

A minimal example:

declare([w0], constant);
depends(P0, [T0, T1]);
O0sol:[diff(P0,T0)=w0];

ex1:subst(O0sol, diff(P0,T0));
ex2:subst(O0sol, diff(P0,T0,2));
ex3:subst(O0sol, diff(diff(P0,T0),T1));
ex4:subst(O0sol, diff(diff(P0,T1),T0));

Out of these, only ex1 evaluates to w0 correctly. All the remaining have to be zeros but I'm unable to force it to be zeros.

I will appreciate any help.

Solution

  • Okay I figured this out myself. Turns out that there's a parameter derivsubst that controls exactly this behavior (see https://maxima.sourceforge.io/docs/manual/maxima_101.html). I don't understand why this has to be false by default; I'm making it a point to set it to true in everything now.

    The above example works with:

    derivsubst:true$
declare([w0], constant);
depends(P0, [T0, T1]);
O0sol:[diff(P0,T0)=w0];

ex1:subst(O0sol, diff(P0,T0));
ex2:subst(O0sol, diff(P0,T0,2));
ex3:subst(O0sol, diff(diff(P0,T0),T1));
ex4:subst(O0sol, diff(diff(P0,T1),T0));