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.

翻译：芳香双复形是一种基于芳香Butcher树的代数工具，尤其用于显式描述保体积仿射等变数值积分器。本研究借鉴变分法理论，在芳香森林的框架下定义了李导数、不同对称性概念及诺特理论等新工具。该方法能够建立芳香保体积方法与欧拉-拉格朗日复形上对称性之间的对应关系，在芳香背景下阐述诺特定理，并通过李导数显式描述保体积方法的芳香B级数。