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The regular representation of the radical of a differential ideal has various applications such as solving the membership problem, computing Taylor expansion of solutions, finding the Lie symmetries, and solving dynamical systems. Presently, there is no algorithm giving all regular representations for all possible values of the parameters for a polynomial differential ideal with parametric coefficients. In this article, we propose a new algorithm that computes all different regulardoi:10.1080/25742558.2018.1507131 fatcat:kwosy23c7bhqzjafhqj66jwj6y