  Dimensional reduction of theories involving (super-)gravity gives rise to
sigma models on coset spaces of the form G/H, with G a non-compact group, and H
its maximal compact subgroup. The reverse process, called oxidation, is the
reconstruction of the possible higher dimensional theories, given the lower
dimensional theory. In 3 dimensions, all degrees of freedom can be dualized to
scalars. Given the group G for a 3 dimensional sigma model on the coset G/H, we
demonstrate an efficient method for recovering the higher dimensional theories,
essentially by decomposition into subgroups. The equations of motion, Bianchi
identities, Kaluza-Klein modifications and Chern-Simons terms are easily
extracted from the root lattice of the group G. We briefly discuss some aspects
of oxidation from the E_{8(8)}/SO(16) coset, and demonstrate that our formalism
reproduces the Chern-Simons term of 11-d supergravity, knows about the
T-duality of IIA and IIB theory, and easily deals with self-dual tensors, like
the 5-tensor of IIB supergravity.
