A Lie Algebraic Approach Jan Sanders Wiskunde en Informatica, Vrije Universiteit Amsterdam e-mail: jansa@can.nl Two examples are given of algorithms based on the imbedding in a Lie algebra of a given linear operator. The first is the computation of non-semisimple normal forms of systems at equilibrium, using sl(2) and the second the computation of e.g. conservation laws of PDEs using the 3 dimensional Heisenberg algebra as an extension of the total differentiation operator. Both algorithms have been implemented in Maple programs producing Form code.