Juggling with tensor bases in functional approaches

Systematic expansion schemes in functional approaches require the inclusion of non-classical tensor structures for relevant vertices. Each vertex has to be expanded in an appropriate tensor basis with a rapidly increasing number of basis elements. In contrast, classical actions typically only contain one of many tensor structures of a given vertex. Among the related tasks are the construction of bases and projection operators, the importance ordering of their elements, and the optimisation of such tensor bases, as well as an analysis of their regularity in momentum space. We present progress in all these directions and introduce the Mathematica package TensorBases designed for the aforementioned tasks.