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Two programs, feyngen and feyncop, were developed. feyngen is designed togenerate high loop order Feynman graphs for Yang-Mills, QED and $\phi^k$theories. feyncop can compute the coproduct of these graphs on the underlyingHopf algebra of Feynman graphs. The programs can be validated by exploitingzero dimensional field theory combinatorics and identities on the Hopf algebrawhich follow from the renormalizability of the theories. A benchmark for bothprograms was made.

Computations and generation of elements on the Hopf algebra of Feynman graphs