Finding Linear Dependencies in Integration-By-Parts Equations: A Monte Carlo Approach

doi:10.1145/321784.321787

M. T. McClellan, The exact solution of systems of linear equations with polynomial coefficients, J. ACM 20 (4) (1973) 563–588 · 1973

Earlier work this paper cites.

doi:http://dx.doi.org/10.1016/0020-0190(78)90067-4

R. A. Demillo, R. J. Lipton, A probabilistic remark on algebraic program testing, Information Processing Letters 7 (4) (1978) 193 – 195 · 1978

Earlier work this paper cites.

doi:10.1007/3-540-09519-5_73

R. Zippel, Probabilistic algorithms for sparse polynomials, in: E. Ng (Ed.), Symbolic and Algebraic Computation, Vol. 72 of Lecture Notes in Computer Science, Springer Berlin Heidelberg, 1979, pp. 216–226 · 1979

Earlier work this paper cites.

J. T. Schwartz, Fast probabilistic algorithms for verification of polynomial identities, Journal of the ACM (JACM) 27 (4) (1980) 701–717

1980

Earlier work this paper cites.

doi:10.1016/0370-2693(81)90288-4

F. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions, Phys.Lett. B100 (1981) 65–68 · 1981

Earlier work this paper cites.

doi:10.1016/0550-3213(81)90199-1

K. Chetyrkin, F. Tkachov, Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops, Nucl.Phys. B192 (1981) 159–204 · 1981

Earlier work this paper cites.

K. Geddes, S. Czapor, G. Labahn, Algorithms for computer algebra, Kluwer Acad., Boston [u.a.], 1992

1992

Earlier work this paper cites.

doi:10.1007/BF01559486

D. J. Broadhurst, Three loop on-shell charge renormalization without integration: Lambda-MS (QED) to four loops, Z.Phys. C54 (1992) 599–606 · 1992

Earlier work this paper cites.

R. E. Zippel, Effective polynomial computation, Vol. 241, Springer, 1993

1993

Cited alongside, same era.

arXiv:hep-ph/9512442

L. V. Avdeev, Recurrence relations for three loop prototypes of bubble diagrams with a mass, Comput.Phys.Commun. 98 (1996) 15–19 · 1996

Cited alongside, same era.

doi:10.1016/S0304-3975(97)00065-0

J. Karczmarczuk, Generating power of lazy semantics, Theor. Comput. Sci. 187 (1-2) (1997) 203–219 · 1997

Cited alongside, same era.

L. Karczmarczuk, Scientific computation and functional programming, Computing in Science & Engineering 1 (3) (1999) 64–72

1999

Cited alongside, same era.

arXiv:hep-ph/9912329

T. Gehrmann, E. Remiddi, Differential equations for two loop four point functions, Nucl.Phys. B580 (2000) 485–518 · 2000

Cited alongside, same era.

arXiv:hep-ph/0102033

S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int.J.Mod.Phys. A15 (2000) 5087–5159 · 2000

S. Peyton-Jones, Haskell 98 language and libraries : the revised report , Cambridge University Press, Cambridge U.K. ;;New York, 2003. URL http://www.worldcat.org/isbn/9780521826143

2003

Later among the works it cites.

arXiv:hep-ph/0404258

C. Anastasiou, A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations, JHEP 0407 (2004) 046 · 2004

Later among the works it cites.

arXiv:hep-ph/0503209

Y. Schroder, A. Vuorinen, High-precision epsilon expansions of single-mass-scale four-loop vacuum bubbles, JHEP 0506 (2005) 051 · 2005

Later among the works it cites.

arXiv:0807.3243

Original

A. Smirnov, Algorithm FIRE – Feynman Integral REduction, JHEP 0810 (2008) 107 · 2008

Later among the works it cites.

arXiv:0804.3008

Original

R. Lee, Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals, JHEP 0807 (2008) 031 · 2008