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In this paper, we introduce a new open-source code to find numericalsolutions for the neutrino evolution considering neutrino-neutrinointeractions, which result in the so-called collective effects. We firstdescribe the theoretical background of this type of evolution, explaining thepolarization vector formalism in which we implement our numerical code. We thenshow the results for different neutrino systems. In this first paper, we focuson the case of an isotropic neutrino gas, exploring a mono-energetic scenarioand one with a spectral distribution. The resulting code of this work isavailable at https://github.com/pedrodedin/Neutrino-Collective-Effects.

Open-Source Numerical Solver for Neutrino Collective Effects -- I: Isotropic Neutrino Gas