  In this paper, the Lorentz covariance of algorithms is introduced. Under
Lorentz transformation, both the form and performance of a Lorentz covariant
algorithm are invariant. To acquire the advantages of symplectic algorithms and
Lorentz covariance, a general procedure for constructing Lorentz covariant
canonical symplectic algorithms (LCCSA) is provided, based on which an explicit
LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses
Lorentz invariance as well as long-term numerical accuracy and stability, due
to the preservation of discrete symplectic structure and Lorentz symmetry of
the system. For situations with time-dependent electromagnetic fields, which is
difficult to handle in traditional construction procedures of symplectic
algorithms, LCCSA provides a perfect explicit canonical symplectic solution by
implementing the discretization in 4-spacetime. We also show that LCCSA has
built-in energy-based adaptive time steps, which can optimize the computation
performance when the Lorentz factor varies.
