  Nuclear matter properties based on a relativistic approach suitable for the
description of multi-component systems are calculated. We use a set of nuclear
relativistic mean-field models that satisfy acceptable nuclear matter
properties and neutron star observations. The effects of the density dependence
of the symmetry energy and of the Landau quantization due to the presence of a
strong external magnetic field are discussed. Properties such as the proton
fraction, the Landau mass, Landau parameters and entrainment matrix, the
adiabatic index and speed of sound are calculated for cold $\beta$-equilibrium
matter. A large dispersion on the calculated properties is obtained at two to
three times saturation density $\rho_0 $. The proton Landau mass can be as low
as one third of the vacuum nucleon mass at 2-3$~\rho_0 $. Similar effects are
obtained for the Landau parameters, in particular, the ones involving protons,
where the relative dispersion of $F^0_{pp}$ and $F^1_{pp}$ is as high as 30\%
to 50\% at 2-3$~\rho_0 $. These parameters are particularly sensitive to the
symmetry energy. The effect of the magnetic field on the nuclear properties is
small for fields as high as 10$^{18}$G except for a small range of densities
just above the crust-core transition. Tables with the EoS, and the parameters,
are provided in the Supplementary Material section.
