In his article “Subscripts as Partial Differentiation Operatuuors” , rlopez 1228 showed us a way to denote partial derivatives by repeat subscripts. For example, the sixth derivative of u(x,y) with respect to x will be denoted by u_{x,x,x,x,x,x}.

Is there a way to make the notation u_{x,x,x,x,x,x} even shorter by u_{6x}?

In the same way mixed derivatives u_{x,x,x,y,y,y,y} will be denoted as u_{3x,4y}, etc.

Thank you very much!

I am trying to write procedures in MAPLE to deal with pseudo differential operators such as P=1+f_1D^{-1}+f_2D^{-2}+f_3D^{-3}+...,  where D=d/dx, f_i are functions of x. D^n for n<=0 work like usual differetial operators for n>=0. For example D^nD^m=D^{m+n}, D^n f=\sum_{i>=0}\binom{n}{i}(D^i f)D^{n-i}, where \binom{n}{i} are binomial coefficients given by n(n-1)...(n-i+1)/i! for n<= 0. I am wondering which package in MAPLE I could begin with, and how can I define D^{-1} and generally D^{-n}.

Thank you very much!

I am very new to Maple. I would be very grateful if someone could teach me how to write a command in an Maple worksheet to do the following:

Let u(x) be a function of x.

How can I introduce an abbreviation of derivatives so u1x (or u_{1x}) is the first derivative of u(x) with respect to x, i.e., u1x=\partial u/\partial x; u2x (or u_{2x}) is the second derivative of u(x) with respect to x, i.e., u2x=\partial^2 u/\partial x^2; u3x (or u_{3x}) is the third derivative of u(x...