  Let $(S,*)$ be an involutive local ring and let $U(2m,S)$ be the unitary
group associated to a nondegenerate skew hermitian form defined on a free
$S$-module of rank $2m$. A presentation of $U(2m,S)$ is given in terms of
Bruhat generators and their relations. This presentation is used to construct
an explicit Weil representation of the symplectic group $Sp(2m,R)$ when $S=R$
is commutative and $*$ is the identity.
  When $S$ is commutative but $*$ is arbitrary with fixed ring $R$, an
elementary proof that the special unitary group $SU(2m,S)$ is generated by
unitary transvections is given. This is used to prove that the reduction
homomorphisms $SU(2m,S)\to SU(2m,\tilde{S})$ and $U(2m,S)\to U(2m,\tilde{S})$
are surjective for any factor ring $\tilde{S}$ of $S$. The corresponding
results for the symplectic group $Sp(2m,R)$ are obtained as corollaries when
$*$ is the identity.
