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We provide a framework for generic 4D conformal bootstrap computations. It isbased on the unification of two independent approaches, the covariant(embedding) formalism and the non-covariant (conformal frame) formalism. Weconstruct their main ingredients (tensor structures and differential operators)and establish a precise connection between them. We supplement the discussionby additional details like classification of tensor structures of n-pointfunctions, normalization of 2-point functions and seed conformal blocks,Casimir differential operators and treatment of conserved operators andpermutation symmetries. Finally, we implement our framework in a Mathematicapackage and make it freely available.

General Bootstrap Equations in 4D CFTs