We study a new representation of non-linear multivariate equations for algebraic cryptanalysis. Using a combination of multiple right hand side equations and binary decision diagrams, our new representation allows a very efficient conjunction of a large number of separate equations. We apply our new technique to the stream cipher Trivium and variants of Trivium reduced in size. By merging all equations into one single constraint, manageable in size and processing time, we get a representation of the Trivium cipher as one single equation.