[jacobolus]

And if you use a formalism accepting general multivectors, you get 1 equation.

The fully expanded coordinate version is based on an arbitrary choice of spacetime coordinates.

Ideally you'd use a computer language/environment with a rich enough basic formalism to let you write the 1 formula in a human-legible way and have your compiler expand out all of the coordinate version as appropriate for the particular problem for the sake of doing floating point arithmetic.