A new generating-function framework turns IBP relations into differential equations in a non-commutative algebra, yielding an iterative algorithm that derives symbolic reduction rules and checks completeness for topologies such as the sunset and double-box diagrams.
Refining integration-by-parts reduction of feynman integrals with machine learning
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Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.