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In this paper, we construct a uniform formula that can iteratively reduce allauxiliary scalar product numerators of arbitrary multi-loop Feynman integrals.Integrals with such numerators commonly appear in Integration-By-Parts (IBP)relations. This formula is constructed with the generalized Sylvester'sdeterminant identity. Compared to that using only traditional IBP reductionmethod, the combination of the formula and the traditional IBP method shows asignificant speed-up.

Iteratively Reduce Auxiliary Scalar Product in Multi-loop Integrals