We use generalized unitarity at the integrand-level to directly constructlocal, manifestly dual-conformally invariant formulae for all two-loopscattering amplitudes in planar, maximally supersymmetric Yang-Mills theory(SYM). This representation separates contributions into manifestly finite anddivergent terms---in a way that makes manifest the exponentiation of infrareddivergences at the integrand-level. These results perfectly match the all-loopBCFW recursion relations, to which we provide a closed-form solution validthrough two-loop-order. Finally, we describe and document a Mathematica packagewhich implements these results, available as part of this work's source fileson the arXiv.
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