@Carl Love I apologize — I’ve been quite busy lately. I actually didn’t end up using the code since I’ve decided to go an alternative route. I do appreciate the time that you’ve spent on it though.

@Carl Love Thank you for the package! Now how do I go about using it? (Sorry — I’m fairly new to Maple). Also, is it possible to modify the old code to so it does transform the subsequent variables?

@Carl Love I got it working by using your code as a template. However, for some reason, when I do VuReduce(v[0]²v[1]u[0]) it doesn't run the procedure on v[1]*u[0]. It just outputs v[0]²v[1]u[0]. Other than that, it's working great!

@Carl Love In practice, this is computing v[0]^2*u[0]^2 using the VuReduce procedure and manually replacing the other variables. Hopefully this gives a better idea at what I'm trying to aim for...

@Carl Love Yes, they can be split apart in that way so only 3 would be necessary. However, since I’ve been replacing manually, it’s been easier to use the six different procedures rather than split apart the variables.

So v[0]^3*u[0] = v[0]^2*v[0]*u[0] = v[0]^2*Vu(0,0,1). The value of Vu(0,0,1) is u[0]*v[0]+2w[0]. So we have v[0]^2*(u[0]*v[0]+2w[0]). Then distribute and repeat the process until the variables are in the order of u, v, w.

@Carl Love All at one time if possible...

@Carl Love Thank you so much... This is exactly what I'm needing -- I'm speechless! There is one final caveat... I was hoping to be able to adapt this code and figure it out, but I want to make sure it's correct!

I have more than one procedure... So this works for Vu(a, b, c) which corresponds to variables of the form v_a^c u_b 

However, the other procedures are vU(a, b, c) for variables like v_a u_b^c (Notice how the power appears on the variable that's capitalized in the procedure). And likewise Wv(a, b, c) for w_a^c v_b , wV(a, b, c) for w_a v_b^c, Wu(a, b, c) for w_a^c u_b, and wU(a, b, c) for w_a u_b^c

As you may notice, the procedure Vu(0,0,1) and uV(0,0,1) produce the same result since they're both v₀u₀. I might be dealing with an expression like this where I'm needing to replace multiple variables: w₀²u₀v₂u₀²w₀v₁. So the corresponding replacements would be:

Wu(0,0,2)vU(2,0,2)Wv(0,1,1). Does that make sense?

Thank you so much for your help!

@Carl Love Thank you for your reply. Firstly, they are subscripted like v[a]. The exponent c is non-zero; it’s a natural number. I’m currently using the Physics package:

with(Physics)

setup(Noncommutativeprefix = {u, v, w})

This makes Maple view v[a] u[b] as different from u[b] v[a]. 

What you have on 4 is exactly what I’m needing. Essentially, for every occurrence of a variable of that form, I want to replace it with that procedure.

Thanks again for your help!