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The long life-time of the quark-gluon plasma likely to be created in therelativistic heavy ion collisions at RHIC and LHC energies renders it sensitiveto the details of the equation of state of the quark-matter. We show that the$p_T$ dependence of the survival probability of the directly produced $J/\psi$at RHIC energies and that of the directly produced $\Upsilon$ at LHC energiesis quite sensitive to the speed of sound in the quark matter, which relates thepressure and the energy density of the plasma. The transverse expansion of theplasma is shown to strongly affect the $J/\psi$ suppression at LHC energies.Comment: 26 pages including 11 figures. (Submitted to Eur. Phys. Jour. C

Determination of the equation of state of quark matter from $J/\psi$ and $\Upsilon$ suppression at RHIC and LHC