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TARDIS creates synthetic spectra for supernova ejecta and is sufficiently fast to allow exploration of the complex parameter spaces of models for SN ejecta. TARDIS uses Monte Carlo methods to obtain a self-consistent description of the plasma state and to compute a synthetic spectrum. It is written in Python with a modular design that facilitates the implementation of a range of physical approximations that can be compared to assess both accuracy and computational expediency; this allows users to choose a level of sophistication appropriate for their application.