Fetching the paper…
Reading the bibliography…
We present $\text{Fuchsia}$ $-$ an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients $\partial_x\,\mathbf{f}(x,\epsilon) = \mathbb{A}(x,\epsilon)\,\mathbf{f}(x,\epsilon)$ finds a basis transformation $\mathbb{T}(x,\epsilon)$, i.e., $\mathbf{f}(x,\epsilon) = \mathbb{T}(x,\epsilon)\,\mathbf{g}(x,\epsilon)$, such that the system turns into the epsilon form: $\partial_x\, \mathbf{g}(x,\epsilon) = \epsilon\,\mathbb{S}(x)\,\mathbf{g}(x,\epsilon)$, where $\mathbb{S}(x)$ is a Fuchsian matrix.
The order of a singularity in fuchs’ theory
J. Moser · 1959
Earlier work this paper cites.
Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops
K. Chetyrkin and F. Tkachov · 1981
Earlier work this paper cites.
Differential equation method: The Calculation of N point Feynman diagrams
A. Kotikov · 1991
Earlier work this paper cites.
Differential equations method: New technique for massive Feynman diagrams calculation
A. Kotikov · 1991
Earlier work this paper cites.
Differential equations method: The Calculation of vertex type Feynman diagrams
A. Kotikov · 1991
Earlier work this paper cites.
An algorithm computing the regular formal solutions of a system of linear differential equations
M. Barkatou and E. Pflügel · 1999
Earlier work this paper cites.
High precision calculation of multiloop Feynman integrals by difference equations
S. Laporta · 2000
Earlier work this paper cites.
Feynman Integral Calculus
V. Smirnov · 2006
Earlier work this paper cites.
Algorithm FIRE – Feynman Integral REduction
A. Smirnov · 2008
Earlier work this paper cites.
Presenting LiteRed: a tool for the Loop InTEgrals REDuction
R. Lee · 2012
Cited alongside, same era.
Reduze 2 - Distributed Feynman Integral Reduction
A. von Manteuffel and C. Studerus · 2012
Cited alongside, same era.
Multiloop integrals in dimensional regularization made simple
J. Henn · 2013
Cited alongside, same era.
FIRE4, LiteRed and accompanying tools to solve integration by parts relations
A. Smirnov and V. Smirnov · 2013
Cited alongside, same era.
LiteRed 1.4: a powerful tool for reduction of multiloop integrals
R. Lee · 2014
FIRE5: a C++ implementation of Feynman Integral REduction
A. Smirnov · 2015
Later among the works it cites.
L. Tancredi · 2015
Later among the works it cites.
J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, and C. Schneider · 2016
Later among the works it cites.
SageMath, the Sage Mathematics Software System (Version 7.0)
The Sage Developers · 2016
Later among the works it cites.
Azurite: An algebraic geometry based package for finding bases of loop integrals
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Maxima, a computer algebra system. version 5.35.1, December 2014
Maxima · 2014
Cited alongside, same era.
Simplified differential equations approach for Master Integrals
C. Papadopoulos · 2014
Cited alongside, same era.
Lectures on differential equations for Feynman integrals
J. Henn · 2015
Cited alongside, same era.
Reducing differential equations for multiloop master integrals
R. Lee · 2015
Cited alongside, same era.
A. Georgoudis, K. J. Larsen, and Y. Zhang · 2016
Later among the works it cites.
Fuchsia and master integrals for splitting functions from differential equations in QCD
O. Gituliar and V. Magerya · 2016
Later among the works it cites.
Evaluating multi-loop Feynman integrals using differential equations: automatizing the transformation to a canonical basis
C. Meyer · 2016
Later among the works it cites.
Transforming differential equations of multi-loop Feynman integrals into canonical form
C. Meyer · 2016
Later among the works it cites.
epsilon: A tool to find a canonical basis of master integrals
M. Prausa · 2017
Closest in time.