On Jul 28, 10:35 am, Simon King <[email protected]> wrote:

> The point is that some people (including myself) believe that
> polynomials belong to algebra, whereas differentiation is calculus. A
> polynomial and a polynomial function are two very different things.
> So, how (and why) would one differentiate a polynomial?

Actually, differentiation of polynomials (just as a formal operation)
has a lot of algebraic meaning, but it's often called "taking
derivative". For example,
GCD(f, f.derivative())
will tell you whether a polynomial has any repeated factors.

This works:

sage: R.<X>=GF(9,'t')[]
sage: (X^2).derivative()

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