A wide literature exists on constraint programming model linearization, based on integer domain decomposition. This paper considers the systematic study of classical global constraints, but in the context of mathematical variables. We consider constraints originally stated using integer domain variables, for which we investigate new definitions and linear decomposi-tions using bounded rational variables. We introduce a generic scheme for reification and softening. Combined with state-of-the-art decompositions on integer variables, this approach permits solving discrete-continuous high level models using a single modeler, connected to a MILP solver. (BEST PAPER AWARD)