FORM version 4.0

Kuipers, Jan; Ueda, Takahiro; Vermaseren, J. A. M.; Vollinga, Jens

doi:10.1016/j.cpc.2012.12.028

Cited by 487 publications

(445 citation statements)

References 14 publications

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“…We thank Lorenzo Tancredi for clarifying discussions and Matthias Kerner for technical support with SecDec. Some of the algebraic manipulations required in this work were carried out with FORM [124]. The Feynman diagrams were generated by FeynArts [125,126] and drawn with Axodraw …”

Section: Acknowledgmentsmentioning

confidence: 99%

Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

Bonciani

Vita

Mastrolia

et al. 2016

J. High Energ. Phys.

105

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We present the calculation of the master integrals needed for the two-loop QCD×EW corrections to q +q → l − + l + and q +q → l − + ν , for massless external particles. We treat the W and Z bosons as degenerate in mass. We identify three types of diagrams, according to the presence of massive internal lines: the no-mass type, the onemass type, and the two-mass type, where all massive propagators, when occurring, contain the same mass value. We find a basis of 49 master integrals and evaluate them with the method of the differential equations. The Magnus exponential is employed to choose a set of master integrals that obeys a canonical system of differential equations. Boundary conditions are found either by matching the solutions onto simpler integrals in special kinematic configurations, or by requiring the regularity of the solution at pseudothresholds. The canonical master integrals are finally given as Taylor series around d = 4 spacetime dimensions, up to order four, with coefficients given in terms of iterated integrals, respectively up to weight four.

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Section: Acknowledgmentsmentioning

confidence: 99%

Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

Bonciani

Vita

Mastrolia

et al. 2016

J. High Energ. Phys.

105

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“…The performance of MCTS-Horner followed by CSE has been tested by implementing it in FORM [26,27]. MCTS-Horner was tested on a variety of different multivariate polynomials, against the currently best algorithms.…”

Section: Sensitivity To C P and Nmentioning

confidence: 99%

“…In this field large equations (often very large) are needed to be solved quickly. Standard packages such as MAPLE and MATHEMATICA are often too slow, and scientists frequently use a specialized highefficiency package called FORM [27].…”

Section: Horner's Rule For Multivariate Polynomialsmentioning

confidence: 99%

Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

Herik

Kuipers

Vermaseren

et al. 2014

Communications in Computer and Information Science

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Abstract. After a computer chess program had defeated the human World Champion in 1997, many researchers turned their attention to the oriental game of Go. It turned out that the minimax approach, so successful in chess, did not work in Go. Instead, after some ten years of intensive research, a new method was developed: MCTS (Monte Carlo Tree Search), with promising results. MCTS works by averaging the results of random play-outs. At first glance it is quite surprising that MCTS works so well. However, deeper analysis revealed the reasons.The success of MCTS in Go caused researchers to apply the method to other domains. In this article we report on experiments with MCTS for finding improved orderings for multivariate Horner schemes, a basic method for evaluating polynomials. We report on initial results, and continue with an investigation into two parameters that guide the MCTS search. Horner's rule turns out to be a fruitful testbed for MCTS, allowing easy experimentation with its parameters. The results reported here provide insight into how and why MCTS works. It will be interesting to see if these insights can be transferred to other domains, for example, back to Go.

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“…In this case one might need to update the PATH and PYTHONPATH environment variables accordingly. The package needs Form-4 [29,30], which should be installed separately by the user, in order to compute the expansions which are needed and for the generation of the corresponding source code.…”

Section: Installationmentioning

confidence: 99%

“…In order to simplify the generation of the numerator expansions and the corresponding source code needed by Ninja as input, we distribute with the library a small Python package called NinjaNumGen which uses Form-4 [28][29][30] in order to compute the expansions and produce an optimized source code which can be used by the library.…”

Section: Introductionmentioning

confidence: 99%

Ninja: Automated integrand reduction via Laurent expansion for one-loop amplitudes

Peraro¹

2014

Computer Physics Communications

145

148

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FORM version 4.0

Cited by 487 publications

References 14 publications

Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

Two-loop master integrals for the mixed EW-QCD virtual corrections to Drell-Yan scattering

Investigations with Monte Carlo Tree Search for Finding Better Multivariate Horner Schemes

Ninja: Automated integrand reduction via Laurent expansion for one-loop amplitudes

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