  The Einstein equations have proven surprisingly difficult to solve
numerically. A standard diagnostic of the problems which plague the field is
the failure of computational schemes to satisfy the constraints, which are
known to be mathematically conserved by the evolution equations. We describe a
new approach to rewriting the constraints as first-order evolution equations,
thereby guaranteeing that they are satisfied to a chosen accuracy by any
discretization scheme. This introduces a set of four subsidiary constraints
which are far simpler than the standard constraint equations, and which should
be more easily conserved in computational applications. We explore the manner
in which the momentum constraints are already incorporated in several existing
formulations of the Einstein equations, and demonstrate the ease with which our
new constraint-conserving approach can be incorporated into these schemes.
