  An $n$-ary integral quadratic form is a formal expression
$Q(x_1,..,x_n)=\sum_{1\leq i,j\leq n}a_{ij}x_ix_j$ in $n$-variables
$x_1,...,x_n$, where $a_{ij}=a_{ji} \in \mathbb{Z}$. We present a randomized
polynomial time algorithm that given a quadratic form $Q(x_1,...,x_n)$, a prime
$p$, and a positive integer $k$ outputs a $\mathtt{U} \in
\text{GL}_n(\mathbb{Z}/p^k\mathbb{Z})$ such that $\mathtt{U}$ transforms $Q$ to
its $p$-adic canonical form.
