Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space

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1901

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S. Abreu, L. J. Dixon, E. Herrmann, B. Page, and M. Zeng, The two-loop five-point amplitude in 𝒩 \mathcal{N} = 8 supergravity

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1901

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A. V. Smirnov and F. S. Chuharev, FIRE6: Feynman Integral REduction with Modular Arithmetic

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1901

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H. Frellesvig, F. Gasparotto, S. Laporta, M. K. Mandal, P. Mastrolia, L. Mattiazzi, and S. Mizera, Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers

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1901

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Y. Wang, Z. Li, and N. Ul Basat, Direct Reduction of Amplitude

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1901

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S. Caron-Huot, L. J. Dixon, F. Dulat, M. von Hippel, A. J. McLeod, and G. Papathanasiou, Six-Gluon Amplitudes in Planar 𝒩 = 4 {\cal N}=4 Super-Yang-Mills Theory at Six and Seven Loops

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1903

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S. Abreu, J. Dormans, F. Febres Cordero, H. Ita, B. Page, and V. Sotnikov, Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD

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1904

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J. Klappert and F. Lange, Reconstructing Rational Functions with FireFly

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1904

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T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs

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1905

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S. Badger, D. Chicherin, T. Gehrmann, G. Heinrich, J. M. Henn, T. Peraro, P. Wasser, Y. Zhang, and S. Zoia, Analytic form of the full two-loop five-gluon all-plus helicity amplitude

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1905

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H. B. Hartanto, S. Badger, C. Brønnum-Hansen, and T. Peraro, A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons

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1906

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H. Frellesvig, F. Gasparotto, M. K. Mandal, P. Mastrolia, L. Mattiazzi, and S. Mizera, Vector Space of Feynman Integrals and Multivariate Intersection Numbers

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1907

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R. Zippel, Probabilistic algorithms for sparse polynomials

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P. A. Baikov, Explicit solutions of the three loop vacuum integral recurrence relations

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S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations

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E. Kaltofen, W.-s. Lee, and A. Lobo, Early Termination in Ben-Or/Tiwari Sparse Interpolation and a Hybrid of Zippel’s Algorithm*

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2001

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A. V. Smirnov, Algorithm FIRE – Feynman Integral REduction

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2008

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L. J. Dixon, J. M. Drummond, and J. M. Henn, Bootstrapping the three-loop hexagon

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2011

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J. Gluza, K. Kajda, and D. A. Kosower, Towards a Basis for Planar Two-Loop Integrals

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2011

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Y. Zhang, Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods

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2012

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P. Mastrolia, E. Mirabella, G. Ossola, and T. Peraro, Scattering Amplitudes from Multivariate Polynomial Division

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2012

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R. M. Schabinger, A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations

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2012

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N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, and J. Trnka, Local Integrals for Planar Scattering Amplitudes

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2012

Cited alongside, same era.

S. Badger, H. Frellesvig, and Y. Zhang, A Two-Loop Five-Gluon Helicity Amplitude in QCD

Original

2013

Cited alongside, same era.

J. M. Henn, Multiloop integrals in dimensional regularization made simple

Original

2013

Cited alongside, same era.

L. J. Dixon, J. M. Drummond, M. von Hippel, and J. Pennington, Hexagon functions and the three-loop remainder function

Original

2013

Cited alongside, same era.

R. N. Lee and A. A. Pomeransky, Critical points and number of master integrals

Original

S. Abreu, F. Febres Cordero, H. Ita, B. Page, and M. Zeng, Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity

Original

2018

Later among the works it cites.

S. Abreu, F. Febres Cordero, H. Ita, B. Page, and V. Sotnikov, Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity

Original

2018

Later among the works it cites.

T. Gehrmann, J. M. Henn, and N. A. Lo Presti, Pentagon functions for massless planar scattering amplitudes

Original

2018

Later among the works it cites.

D. Chicherin, J. Henn, and V. Mitev, Bootstrapping pentagon functions

Original

2018

Later among the works it cites.

P. Maierhoefer, J. Usovitsch, and P. Uwer, Kira - A Feynman Integral Reduction Program