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We describe an efficient implementation of the BCFW recursion relations fortree-amplitudes in N=4 super Yang-Mills, which can generate analytic formulaefor general N^kMHV colour-ordered helicity-amplitudes-which, in particular,includes all those of non-supersymmetric Yang-Mills. This note accompanies thepublic release of the Mathematica package "bcfw", which can quickly (andautomatically) generate these amplitudes in a form that should be easy toexport to any computational framework of interest, or which can be evaluateddirectly within Mathematica given external states specified by four-momenta,spinor-helicity variables or momentum-twistors. Moreover, bcfw is able to solvethe BCFW recursion relations using any one of a three-parameter family ofrecursive `schemes,' leading to an extremely wide variety of distinct analyticrepresentations of any particular amplitude. This flexibility is made possibleby bcfw's use of the momentum-twistor Grassmannian integral to describe alltree amplitudes; and this flexibility is accompanied by a remarkable increasein efficiency, leading to formulae that can be evaluated much faster-often byseveral orders of magnitude-than those previously derived using BCFW.

Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica