@ecterrab Yes, I understand all the caveats.

To do this, I assume that I would need to modify not the regular `print/diff` but rather the `print/diff` that is installed by PDEtools:-declare.

@ecterrab Thanks. I should've checked whether `print/` procedures were traceable.

My goal is to investigate the feasibility of satisfying a recent request on MaplePrimes that subscripted derivatives (as produced by PDEtools:-declare) be printed in an abbreviated form. The Asker wants, for example, that f[x,x,x,x,x,x] print as f[`6x`] and that f[x,x,x,y,y,y,y] print as f[`3x`,`4y`] or perhaps f[`3x4y`].

@Muhammad Usman Your file still did not attach.

I guess it was the same file as your other question, which did attach, so don't bother responding here. You should delete this question.

@Muhammad Usman Your file did not attach. Please try again.

I don't understand what you want. Could you give an example of the final form of the matrix that you want? If we restrict the rows and columns of L and F to just those that contain M and r, the result will not be square.

@Markiyan Hirnyk The original function omega_i appears (from the graph) to have a singularity at R_i_t = 1. If we avoid this point, then the minimax approximation is much better. I used minimax(omega_i, R_i_t= 0.25..0.95, 3).

@taro yamada The help page for `` is ?emptysymbol .

@Markiyan Hirnyk I was supposing that n would be defined at the time that the OP used the code. If n has a numeric value, then add and mul will not give an error.

@raveen Your book is right. The correctness of that answer is easily verified. But how it is different from the answer that you got with Maple?

@dipamilo What evidence do you have that it uses a numerical method? When given symbolic input doesn't it always give symbolic output?

@Kitonum Why use the curly braces? It could just be f[`6x`], etc. For the double index, I'd prefer f[`3x`,`4y`] over f[`3x,4y`].

@abbeykabir Closed form:

dsolve({diff(y(x),x)=x/y(x), y(0)=-2});

Euler:

sol:= dsolve({diff(y(x),x)=x/y(x), y(0)=-2}, numeric,
     method= classical[foreuler], stepsize= 0.1):
sol(1), sol(7/4), sol(2);

Runge-Kutta:

sol:= dsolve({diff(y(x),x)=x/y(x), y(0)=-2}, numeric,
     method= classical[rk4], stepsize= 0.1):
sol(1), sol(7/4), sol(2);

@yasemin In your original post, you use the command VigenereKeyFind(c). Is that the command that produces output "aaaaaaaaaaaaa"? The argument c should be a string. Perhaps you mean VigenereKeyFind("c"). Otherwise, you should have assigned a string to c.

@Julesp The tickmarks can be typeset in the way that you want like this:

plots:-densityplot(
     10^x*exp(-(10^x)^2-y^2), x= log10(.01)..log10(10), y= -2..2,
     axis[1]= [tickmarks= [seq(k = 10^nprintf("%d", k), k= -2..1)]],
     colorstyle= HUE, axes= boxed, style= patchnogrid, grid= [100,100]
);

I also changed colorstyle from RGB to HUE. This gives much better differentiation.

@Markiyan Hirnyk Sure. Let's take the example that you used:

plots:-densityplot(x*exp(-x^2-y^2), x= 0.01..10, y= -2..2);

which I've modified slightly so that 0 is not the lower bound of x. We change the command to

plots:-densityplot(
     10^x*exp(-(10^x)^2-y^2), x= log10(.01)..log10(10), y= -2..2,
     axis[1]= [tickmarks= map(x-> log10(x)=x, [.01,.1,1,10])],
     colorstyle= RGB, axes= boxed
);