We propose a systematic scheme for computing the variation of rearrangement multilinear functionals arising in the recently developed spectral geometry on noncommutative tori and \(\theta \) -deformed Riemannian manifolds. It can be summarized as a category whose objects consist of spectral functions of the rearrangement multilinear functionals and morphisms are generated by transformations associated with basic operations of the variational calculus. The generators of the morphisms fulfill most, but not all of the relations in Connes’s cyclic category. Compare-and-contrast with, cyclic theory and Hopf cyclic theory have also been discussed.
