  Conservative numerical schemes for general relativistic magnetohydrodynamics
(GRMHD) require a method for transforming between ``conserved'' variables such
as momentum and energy density and ``primitive'' variables such as rest-mass
density, internal energy, and components of the four-velocity. The forward
transformation (primitive to conserved) has a closed-form solution, but the
inverse transformation (conserved to primitive) requires the solution of a set
of five nonlinear equations. Here we discuss the mathematical properties of the
inverse transformation and present six numerical methods for performing the
inversion. The first method solves the full set of five nonlinear equations
directly using a Newton-Raphson scheme and a guess from the previous timestep.
The other methods reduce the five nonlinear equations to either one or two
nonlinear equations that are solved numerically. Comparisons between the
methods are made using a survey over phase space, a two-dimensional explosion
problem, and a general relativistic MHD accretion disk simulation. The run-time
of the methods is also examined. Code implementing the schemes is available for
download on the web.
