Scaling up to multivariate rational function reconstruction

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I present an algorithm for the reconstruction of multivariate rational functions from black-box probes. The arguably most important application in high-energy physics is the calculation of multi-loop and multi-leg amplitudes, where rational functions appear as coefficients in the integration-by-parts reduction to basis integrals. I show that for a dense coefficient the algorithm is nearly optimal, in the sense that the number of required probes is close to the number of unknowns.

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