    SparsePolyOps
      Copyright (c)  2017 John Abbott, Anna M. Bigatti
      GNU Free Documentation License, Version 1.2
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== Examples ==[examples]
%----------------------------------------------------------------------
- [ex-SparsePolyOps1.C ../../examples/index.html#ex-SparsePolyOps1.C]
-

== User documentation ==
%======================================================================

This file offers some useful functions on polynomials.


=== Operations ===[operations]
%----------------------------------------------------------------------

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``.



== Maintainer documentation ==
%======================================================================

Relatively straightforward.  Could be neater and more efficient
(but I can't be bothered to make the changes).


== Bugs, shortcomings and other ideas ==
%======================================================================

Some fns make wasteful copies of coeffs -- probably not important,
but irritating.


== Main changes ==
%======================================================================

**2017**
- September (v0.99557): first release



