Can someone suggest some online Mathematica codes/packages that deal with performing standard CFT computations like OPE expansions, computing different conformal blocks etc.
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A page by an associate professor at Brandeis University has provided a notebook to implement the Virasoro algebra in Mathematica, and compute conformal blocks. It can also teach Mathematica other operator algebras.
This paper also provides ancillary files which include notebooks that can be used to compute conformal blocks using an alternate method built upon in the paper.
Operator Product Expansion
A Mathematica package provides a means to compute crossing matrices and OPEs for special cases involving degenerate operators.
Finally, a package called Lambda has been designed to calculate $\lambda$-brackets, which can be related directly to show they are equivalent to evaluating OPEs for $d=2$ CFTs.
A bunch of files here and elsewhere on the site of the Mathematica summer school provides exercises and Mathematica notebooks which involve applying the conformal bootstrap. This includes the decomposition of conformal blocks and working in $d=4-\epsilon$ dimensions.