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We present a new method to construct integration-by-part (IBP) identitiesfrom the viewpoint of differential geometry. Vectors for generating IBPidentities are reformulated as differential forms, via Poincar\'{e} duality.Using the tools of differential geometry and commutative algebra, we canefficiently find differential forms which generate on-shell IBP relationwithout doubled propagator. Various $D=4$ two-loop examples are presented.

Integration-by-parts identities from the viewpoint of differential geometry