Related papers: Reduze - Feynman Integral Reduction in C++
Program reduction is a technique for simplifying large, failure-inducing programs into minimal reproducible test cases. Language-specific tools such as CReduce achieve strong performance by leveraging deep semantic knowledge of C/C++, but…
RTNeural is a neural inferencing library written in C++. RTNeural is designed to be used in systems with hard real-time constraints, with additional emphasis on speed, flexibility, size, and convenience. The motivation and design of the…
Integration-by-parts reductions of Feynman integrals pose a frequent bottle-neck in state-of-the-art calculations in theoretical particle and gravitational-wave physics, and rely on heuristic approaches for selecting integration-by-parts…
Reduction-based interpreters are traditionally defined in terms of a one-step reduction function which systematically decomposes a term into a potential redex and context, contracts the redex, and recomposes it to construct the new term to…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
The snags in Nucci(1996)REDUCE algorithm are the intrinsic computational efforts and the ability to recognize the ignorable variable(s) during the reduction process of the algorithm. An inappropriate choice of the ignorable variable(s)may…
We report on three improvements in the context of Feynman integral reduction and $\varepsilon$-factorised differential equations: Firstly, we show that with a specific choice of prefactors, we trivialise the $\varepsilon$-dependence of the…
In this note, we introduce the new tool reSolve, a Monte Carlo differential cross-section and parton-level event generator whose main purpose is to add transverse momentum resummation to a general class of inclusive processes at hadron…
The article deals with a kind of recursive function templates in C++, where the recursion is realized corresponding template parameters to achieve better computational performance. Some specialization of these template functions ends the…
We introduce the C++ library Wedge, based on GiNaC, for symbolic computations in differential geometry. We show how Wedge makes it possible to use the language C++ to perform such computations, and illustrate some advantages of this…
Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment…
The standard procedure when evaluating integrals of a given family of Feynman integrals, corresponding to some Feynman graph, is to construct an algorithm which provides the possibility to write any particular integral as a linear…
In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in…
A powerful approach to computing Feynman integrals or cosmological correlators is to consider them as solution to systems of differential equations. Often these can be chosen to be Gelfand-Kapranov-Zelevinsky (GKZ) systems. However, their…
Mathematica package LiteRed is described. It performs the heuristic search of the symbolic IBP reduction rules for loop integrals. It implements also several convenient tools for the search of the symmetry relations, construction of the…
We present a new algorithm for the reduction of one-loop tensor Feynman integrals within the framework of the XLOOPS project, covering both mathematical and programming aspects. The new algorithm supplies a clean way to reduce the one-loop…
We present a historiographical review of algorithms and computer codes developed for solving integration-by-parts relations for Feynman integrals. This procedure is one of the key steps in the evaluation of Feynman integrals, since it…
We provide open-source software implemented in MATLAB, that performs Fourier-Motzkin elimination (FME) and removes constraints that are redundant due to Shannon-type inequalities (STIs). The FME is often used in information theoretic…
We present an efficient graphical approach to construct projectors for the tensor reduction of multi-loop Feynman integrals with both Lorentz and spinor indices in $D$ dimensions. An ansatz for the projectors is constructed making use of…