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