**Abstract:** A method is presented to construct nonconvex
free energies that are invariant under a symmetry
group. Algebraic and geometric methods are used to determine
invariant functions with the right location of minimizers. The
methods are illustrated for symmetry-breaking martensitic phase
transformations. Computer algebra is used to compute a basis of
the corresponding class of invariant functions. Several phase
transitions, such as cubic-to-orthorhombic, are discussed. An
explicit example of an energy for the cubic-to-tetragonal phase
transition is given.