  We introduce an invertible operation on finite sequences of positive integers
and call it "kneading". Kneading preserves three invariants of sequences -- the
parity of the length, the sum of the entries, and one we call the "alternant".
We provide a bijection between the set of sequences with alternant $a$ and
parity $s$ and the set of Zagier-reduced indefinite binary quadratic forms with
discriminant $a^2 + (-1)^s \cdot 4$, and show that kneading corresponds to
Zagier reduction of the corresponding forms. It follows that the sum of a
sequence is a class invariant of the corresponding form. We conclude with some
observations and conjectures concerning this new invariant.
