Hyperbolic plane (awaiting review)

The hyperbolic plane $U$ is the integral lattice with Gram matrix \[ \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}. \] Over a field with characteristic not $2$, every nondegenerate indefinite quadratic space is isometric to a direct sum of a definite quadratic space and some number of copies of the hyperbolic plane. A version also holds for even unimodular lattices, which can be written as $U^{\oplus r} \oplus E_8^{\oplus s}$ or $U^{\oplus r} \oplus E_8(-1)^{\oplus s}$. But this direct sum decomposition does not hold for lattices.