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In the past years the method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals. This method relies on the choice of a basis of master integrals in which the dependence on the dimensional regulator factorizes. We will present an algorithm, which automatizes the transformation to such a basis, starting from some basis that is, for instance, obtained by the usual integration-by-parts reduction techniques. Our algorithm only requires some mild assumptions about the reduction basis. In particular, it applies to problems with multiple scales and rational dependence on the regulator.

Evaluating multi-loop Feynman integrals using differential equations: automatizing the transformation to a canonical basis