  Based on our previous work, we deduce a general formula for pressure of
degenerate and relativistic electrons,Pe, which is suitable for superhigh
magnetic fields, discuss the quantization of Landau levels of electrons, and
consider the quantum electrodynam-ic(QED) effects on the equations of states
(EOSs) for different matter systems. The main conclusions are as follows:Pe is
related to the magnetic field B, matter density ?, and electron fraction Ye ;
the stronger the magnetic field, the higher the electron pressure becomes; the
high electron pressure could be caused by high Fermi energy of electrons in a
superhigh magnetic field; compared with a common radio pulsar, a magnetar could
be a more compact oblate spheroid-like deformed neutron star due to the
anisotropic total pressure; and an increase in the maximum mass of a magnetar
is expected because of the positive contribution of the magnetic field energy
to the EOS of the star.
