OPERA: A Toolbox For Loop Parallelization. This paper presents the mathematical notions for the parallelization of DO-Loops used in the tool OPERA currently under development in our team. It aims at giving the user an environment to parallelize problems described by systems of parameterized affine recurrence equations which formalize single-assignment loop nests. The parallelization technique used in OPERA is based on a classical linear spacextime transformation. Its objectives are to visualize the affine dependences of a problem and to propose a set of different parallel solutions depending on various architectural constraints.