@ecterrab
there is always the issue of who is the prime variable
I think for ode's initial conditions, this is not needed to know? The input for ode IC is (using the D notation) is D(y)(x0)=y0 this can be translated to y'(x0)=y0 without the need to know the independent variable. Isn't this correct? When using eval() notation, no need to change that at all. For second order, the same, (D@@2)(y)(x0)=y0 can be translated to y''(x0)=y0 and so on. For non-integer order, such as nth order (D@@n)(y)(x0)=y0 is translated to y^(n)(x0)=y0
For PDE's, I did not know about ToJet. Thanks for the link. But that only works for the actual PDE, not for initial/boundary conditions. I could not make it translate PDE initial or boundary conditions.
For example,
pde := diff(u(x, y, t), t) = diff(u(x, y, t), x$2)+diff(u(x, y, t), y$2) - u(x,y,t);
Physics:-Latex(PDEtools:-ToJet(pde,u(x,y,t)));
works and gives
(although a better notation is not to use the comma there and just have it as
But can't use ToJet for initial/boundary conditions
bc:=(D[1](u))(0, y, t) = 0;
Physics:-Latex(bc);
But
PDEtools:-ToJet(bc,u(x,y,t));
gives error, since dependent variable now does not work
Error, (in PDEtools:-ToJet) found functions to be rewritten in jet notation, {u(0, y, t)}, having different dependency than the indicated in [u(x, y, t)]
And can not use PDEtools:-ToJet(bc,u(0,y,t)); it gives error.
The notation I like for initial/boundary conditions for PDE's are the standard ones as shown in Haberman PDE's books. Here is an example
But for non-initial conditions, for pde's, I like ToJet notations. (Just wish there was no comma in there)
Thank you