  The aromatic bicomplex is an algebraic tool based on aromatic Butcher trees
and used in particular for the explicit description of volume-preserving
affine-equivariant numerical integrators. The present work defines new tools
inspired from variational calculus such as the Lie derivative, different
concepts of symmetries, and Noether's theory in the context of aromatic
forests. The approach allows to draw a correspondence between aromatic
volume-preserving methods and symmetries on the Euler-Lagrange complex, to
write Noether's theorem in the aromatic context, and to describe the aromatic
B-series of volume-preserving methods explicitly with the Lie derivative.
