This file offers some useful functions on polynomials.
Let f be an element of a polynomial ring.
CoeffHeight(f) -- returns the max of the absolute values of the coeffs of f
IsPalindromic(f) -- returns true iff f is palindromic; error if f is not univariate
reverse(f) -- returns x^deg(f)*f(1/x); error if f is not univariate
reverse(f,t) -- returns f with each power product PP replaced t/PP
graeffe(f) -- returns graeffe transformation of univariate f; its roots are the squares of the roots of f.
graeffe3(f) -- returns cubic graeffe transformation of univariate f; its roots are the cubes of the roots of f.
Relatively straightforward. Could be neater and more efficient (but I can't be bothered to make the changes).
Some fns make wasteful copies of coeffs -- probably not important, but irritating.
2017