Built on

H. Frellesvig, F. Gasparotto, S. Laporta, M. K. Mandal, P. Mastrolia, L. Mattiazzi et al., Decomposition of Feynman integrals on the maximal cut by intersection numbers , JHEP 05
Original
1901
Earlier work this paper cites.
A. V. Smirnov and F. S. Chukharev, FIRE6: Feynman Integral REduction with modular arithmetic , Comput. Phys. Commun. 247
Original
1901
Earlier work this paper cites.
Y. Wang, Z. Li and N. ul Basat, Direct reduction of multiloop multiscale scattering amplitudes , Phys. Rev. D 101
Original
1901
Earlier work this paper cites.
J. Klappert and F. Lange, Reconstructing rational functions with FireFly , Comput. Phys. Commun. 247
Original
1904
Earlier work this paper cites.
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , JHEP 07
Original
1905
Earlier work this paper cites.
J. Artz, R. V. Harlander, F. Lange, T. Neumann and M. Prausa, Results and techniques for higher order calculations within the gradient-flow formalism , JHEP 06
Original
1905
Earlier work this paper cites.
F. Moriello, Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops , JHEP 01
Original
1907
Earlier work this paper cites.
H. Frellesvig, F. Gasparotto, M. K. Mandal, P. Mastrolia, L. Mattiazzi and S. Mizera, Vector Space of Feynman Integrals and Multivariate Intersection Numbers , Phys. Rev. Lett. 123
Original
1907
Earlier work this paper cites.
D. Bendle, J. Böhm, W. Decker, A. Georgoudis, F.-J. Pfreundt, M. Rahn et al., Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space , JHEP 02
Original
1908
Earlier work this paper cites.
C. G. Papadopoulos and C. Wever, Internal reduction method for computing Feynman integrals , JHEP 02
Original
1910
Earlier work this paper cites.
X. Guan, X. Liu and Y.-Q. Ma, Complete reduction of integrals in two-loop five-light-parton scattering amplitudes , Chin. Phys. C 44
Original
1912
Earlier work this paper cites.
R. A. DeMillo and R. J. Lipton, A probabilistic remark on algebraic program testing , Inf. Process. Lett. 7
1978
Earlier work this paper cites.
R. Zippel, Probabilistic algorithms for sparse polynomials , Symbolic Algebraic Comp. EUROSAM 1979
1979
Earlier work this paper cites.
J. T. Schwartz, Fast Probabilistic Algorithms for Verification of Polynomial Identities , J. ACM 27
1980
Earlier work this paper cites.
F. V. Tkachov, A theorem on analytical calculability of 4-loop renormalization group functions , Phys. Lett. B 100
1981
Earlier work this paper cites.
K. G. Chetyrkin and F. V. Tkachov, Integration by parts: The algorithm to calculate β \beta -functions in 4 loops , Nucl. Phys. B192
1981
Earlier work this paper cites.
P. S. Wang, A p-adic Algorithm for Univariate Partial Fractions , Proc. ACM Symp. Symbolic Algebraic Comp. 1981
1981
Earlier work this paper cites.
M. Ben-Or and P. Tiwari, A Deterministic Algorithm for Sparse Multivariate Polynomial Interpolation , Proc. ACM Symp. Theory Comp. 20
1988
Earlier work this paper cites.
E. Kaltofen and Lakshman Y., Improved Sparse Multivariate Polynomial Interpolation Algorithms , Symbolic Algebraic Comp. ISSAC 1988
1989
Earlier work this paper cites.
R. Zippel, Interpolating Polynomials from their Values , J. Symb. Comp. 9
1990
Earlier work this paper cites.
C. Sabbah, Lieu des pôles d’un système holonome d’équations aux différences finies , Bulletin de la Société Mathématique de France 120
1992
Earlier work this paper cites.
S. Laporta, High-precision calculation of multiloop Feynman integrals by difference equations , Int.J.Mod.Phys. A15
2000
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two-loop four-point functions , Nucl. Phys. B580
2000
Earlier work this paper cites.

Similar

E. Kaltofen, W.-s. Lee and A. A. Lobo, Early Termination in Ben-Or/Tiwari Sparse Interpolation and a Hybrid of Zippel’s Algorithm , Proc. Int. Symp. Symbolic Algebraic Comp. 2000
2000
Cited alongside, same era.
A. von Manteuffel, E. Panzer and R. M. Schabinger, Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors , Phys. Rev. Lett. 124
Original
2002
Cited alongside, same era.
S. Weinzierl, On the computation of intersection numbers for twisted cocycles , 2002.01930
Original
2002
Cited alongside, same era.
A. V. Smirnov and V. A. Smirnov, How to choose master integrals , Nucl. Phys. B 960
Original
2002
Cited alongside, same era.
J. Usovitsch, Factorization of denominators in integration-by-parts reductions , 2002.08173

Then

J. M. Henn, Multiloop Integrals in Dimensional Regularization Made Simple , Phys. Rev. Lett. 110
Original
2013
Later among the works it cites.
J. von zur Gathen and J. Gerhard, Modern Computer Algebra . Cambridge University Press, third ed., 2013, 10.1017/CBO9781139856065
2013
Later among the works it cites.
M. Argeri, S. Di Vita, P. Mastrolia, E. Mirabella, J. Schlenk, U. Schubert et al., Magnus and Dyson series for Master Integrals , JHEP 03
Original
2014
Later among the works it cites.
P. Kant, Finding linear dependencies in integration-by-parts equations: A Monte Carlo approach , Comput. Phys. Commun. 185
Original
2014
Later among the works it cites.
A. von Manteuffel and R. M. Schabinger, A novel approach to integration by parts reduction , Phys. Lett. B744

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2020

Integral Reduction with Kira 2.0 and Finite Field Methods

Klappert, Jonas, Lange, Fabian, Maierhöfer, Philipp et al.

Understand

We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features.

The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly.
This procedure can be parallelized on computer clusters with MPI.
Furthermore, the support for user-provided systems of equations has been significantly improved.

Built on

H. Frellesvig, F. Gasparotto, S. Laporta, M. K. Mandal, P. Mastrolia, L. Mattiazzi et al., Decomposition of Feynman integrals on the maximal cut by intersection numbers , JHEP 05
Original
1901
Earlier work this paper cites.
A. V. Smirnov and F. S. Chukharev, FIRE6: Feynman Integral REduction with modular arithmetic , Comput. Phys. Commun. 247
Original
1901
Earlier work this paper cites.
Y. Wang, Z. Li and N. ul Basat, Direct reduction of multiloop multiscale scattering amplitudes , Phys. Rev. D 101
Original
1901
Earlier work this paper cites.
J. Klappert and F. Lange, Reconstructing rational functions with FireFly , Comput. Phys. Commun. 247
Original
1904
Earlier work this paper cites.
T. Peraro, FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs , JHEP 07
Original
1905
Earlier work this paper cites.
J. Artz, R. V. Harlander, F. Lange, T. Neumann and M. Prausa, Results and techniques for higher order calculations within the gradient-flow formalism , JHEP 06
Original
1905
Earlier work this paper cites.
F. Moriello, Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops , JHEP 01
Original
1907
Earlier work this paper cites.
H. Frellesvig, F. Gasparotto, M. K. Mandal, P. Mastrolia, L. Mattiazzi and S. Mizera, Vector Space of Feynman Integrals and Multivariate Intersection Numbers , Phys. Rev. Lett. 123
Original
1907
Earlier work this paper cites.
D. Bendle, J. Böhm, W. Decker, A. Georgoudis, F.-J. Pfreundt, M. Rahn et al., Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space , JHEP 02
Original
1908
Earlier work this paper cites.
C. G. Papadopoulos and C. Wever, Internal reduction method for computing Feynman integrals , JHEP 02
Original
1910
Earlier work this paper cites.
X. Guan, X. Liu and Y.-Q. Ma, Complete reduction of integrals in two-loop five-light-parton scattering amplitudes , Chin. Phys. C 44
Original
1912
Earlier work this paper cites.
R. A. DeMillo and R. J. Lipton, A probabilistic remark on algebraic program testing , Inf. Process. Lett. 7
1978
Earlier work this paper cites.
R. Zippel, Probabilistic algorithms for sparse polynomials , Symbolic Algebraic Comp. EUROSAM 1979
1979
Earlier work this paper cites.
J. T. Schwartz, Fast Probabilistic Algorithms for Verification of Polynomial Identities , J. ACM 27
1980
Earlier work this paper cites.
F. V. Tkachov, A theorem on analytical calculability of 4-loop renormalization group functions , Phys. Lett. B 100
1981
Earlier work this paper cites.
K. G. Chetyrkin and F. V. Tkachov, Integration by parts: The algorithm to calculate β \beta -functions in 4 loops , Nucl. Phys. B192
1981
Earlier work this paper cites.
P. S. Wang, A p-adic Algorithm for Univariate Partial Fractions , Proc. ACM Symp. Symbolic Algebraic Comp. 1981
1981
Earlier work this paper cites.
M. Ben-Or and P. Tiwari, A Deterministic Algorithm for Sparse Multivariate Polynomial Interpolation , Proc. ACM Symp. Theory Comp. 20
1988
Earlier work this paper cites.
E. Kaltofen and Lakshman Y., Improved Sparse Multivariate Polynomial Interpolation Algorithms , Symbolic Algebraic Comp. ISSAC 1988
1989
Earlier work this paper cites.
R. Zippel, Interpolating Polynomials from their Values , J. Symb. Comp. 9
1990
Earlier work this paper cites.
C. Sabbah, Lieu des pôles d’un système holonome d’équations aux différences finies , Bulletin de la Société Mathématique de France 120
1992
Earlier work this paper cites.
S. Laporta, High-precision calculation of multiloop Feynman integrals by difference equations , Int.J.Mod.Phys. A15
2000
Earlier work this paper cites.
T. Gehrmann and E. Remiddi, Differential equations for two-loop four-point functions , Nucl. Phys. B580
2000
Earlier work this paper cites.

Similar

E. Kaltofen, W.-s. Lee and A. A. Lobo, Early Termination in Ben-Or/Tiwari Sparse Interpolation and a Hybrid of Zippel’s Algorithm , Proc. Int. Symp. Symbolic Algebraic Comp. 2000
2000
Cited alongside, same era.
A. von Manteuffel, E. Panzer and R. M. Schabinger, Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors , Phys. Rev. Lett. 124
Original
2002
Cited alongside, same era.
S. Weinzierl, On the computation of intersection numbers for twisted cocycles , 2002.01930
Original
2002
Cited alongside, same era.
A. V. Smirnov and V. A. Smirnov, How to choose master integrals , Nucl. Phys. B 960
Original
2002
Cited alongside, same era.
J. Usovitsch, Factorization of denominators in integration-by-parts reductions , 2002.08173

Then

J. M. Henn, Multiloop Integrals in Dimensional Regularization Made Simple , Phys. Rev. Lett. 110
Original
2013
Later among the works it cites.
J. von zur Gathen and J. Gerhard, Modern Computer Algebra . Cambridge University Press, third ed., 2013, 10.1017/CBO9781139856065
2013
Later among the works it cites.
M. Argeri, S. Di Vita, P. Mastrolia, E. Mirabella, J. Schlenk, U. Schubert et al., Magnus and Dyson series for Master Integrals , JHEP 03
Original
2014
Later among the works it cites.
P. Kant, Finding linear dependencies in integration-by-parts equations: A Monte Carlo approach , Comput. Phys. Commun. 185
Original
2014
Later among the works it cites.
A. von Manteuffel and R. M. Schabinger, A novel approach to integration by parts reduction , Phys. Lett. B744

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2002

Cited alongside, same era.

C. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language , J. Symb. Comput. 33

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S. Amoroso et al., Les Houches 2019: Physics at TeV Colliders: Standard Model Working Group Report , in 11th Les Houches Workshop on Physics at TeV Colliders: PhysTeV Les Houches , 3, 2020, 2003.01700

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2003

Cited alongside, same era.

E. Kaltofen and W.-s. Lee, Early termination in sparse interpolation algorithms , J. Symb. Comp. 36

2003

Cited alongside, same era.

J. Klappert, S. Y. Klein and F. Lange, Interpolation of dense and sparse rational functions and other improvements in FireFly , Comput. Phys. Commun. 264

Original

2004

Cited alongside, same era.

C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations , JHEP 07

2004

Cited alongside, same era.

M. Monagan, Maximal Quotient Rational Reconstruction: An Almost Optimal Algorithm for Rational Reconstruction , Proc. Int. Symp. Symbolic Algebraic Comp. 2004

2004

Cited alongside, same era.

A. G. Grozin, Heavy Quark Effective Theory , Springer Tracts Mod. Phys. 201

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Cited alongside, same era.

Original

2015