In this work we present a detailed explanation of the construction of an appropriate equation of state (EoS) for nuclear astrophysics. We use a relativistic model in order to obtain an EoS for neutrally charged matter that extends from very low to high densities, from zero temperature to 100 MeV with proton fractions ranging from 0 (no protons) to 0.6 (asymmetric matter with proton excess). For the achievement of complete convergence, the Sommerfeld approximation is used at low temperatures and the Boltzman distribution for relativistic particles is used in the calculation of the electron properties at very low densities. Photons are also incorporated as blackbody radiation. An extension of this EoS is also presented with the inclusion of strangeness by taking into account the sigma minus hyperon only. Strangeness fractions range from 0.02 to 0.3.
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