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Many multi-loop calculations make use of integration by parts relations to reduce the large number of complicated Feynman integrals that arise in such calculations to a simpler basis of master integrals.
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J. Gluza, K. Kajda, and D. A. Kosower, Towards a Basis for Planar Two-Loop Integrals
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D. Cabarcas and J. Ding, Linear Algebra to Compute Syzygies and Gröbner Bases
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P. Mastrolia and G. Ossola, On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
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D. Bayer and D. Mumford, What can be computed in algebraic geometry?
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