Make methods to return the even or odd polynomials.

[emsr]

  /**
   * Return the even polynomial.
   */
  _Polynomial
  even() const;

  /**
   * Return the odd polynomial.
   */
  _Polynomial
  odd() const;

Underneath you should have:
_Polynomial
thing(int stride, int offset) const;

Conversely, an
eval(int stride, int offset, x)
would be a smart underpinning for eval_even/eval_odd.

[emsr]

Some kind of iterator would be better than a thing to emit polynomials.