Apologies if this is outside of the realm of Mathematica -- I'm still trying to figure out the limits of how expressive Mathematica is (and how much of my work can be automated).
Suppose I define the following:
f = x f[n_] = x * f[n-1]
Then, I want to ask:
for integral k>1, what is the degree of f[k] ?
so for example, I want to write a function:
degreeOf[f, k] = k
Now, I know that in this above example, given that we know how f is defined, it's trivial that degreeOf[f, k] = k. However, is it possible to write generic degreeOf ?
In a sense, I'm curious if the "computational" part of mathematica -- it's ability to handle symbols and do substitutions + simplifications -- or if it can reason about them at a deeper level.