Related papers: FormCalc 8: Better Algebra and Vectorization
Starting from the parametric representation of a Feynman diagram, we obtain it's well defined value in dimensional regularisation by changing the integrals over parameters into contour integrals. That way we eventually arrive at a…
Topological integral transforms have found many applications in shape analysis, from prediction of clinical outcomes in brain cancer to analysis of barley seeds. Using Euler characteristic as a measure, these objects record rich geometric…
pSecDec is a computer tool to evaluate Feynman integrals and their weighted sums (amplitudes) using the method of sector decomposition and numerical integration. The new release of pySecDec version 1.6 comes with a significant performance…
Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness…
We propose that the symbol alphabet for classes of planar, dual-conformal-invariant Feynman integrals can be obtained as truncated cluster algebras purely from their kinematics, which correspond to boundaries of (compactifications of)…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
We present a new version of $\texttt{SecDec}$, a program for the numerical computation of parametric integrals in the context of dimensional regularization. By its modular structure, the $\texttt{python}$ rewrite $\texttt{pySecDec}$ is much…
Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a…
We give a coalgebra structure on 1-vertex irreducible graphs which is that of a cocommutative coassociative graded connected coalgebra. We generalize the coproduct to the algebraic representation of graphs so as to express a bare 1-particle…
We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…
The bilinear combination of Dirac spinors $u(p_1,n_1)\bar u(p_2,n_2)$ is expressed in terms of Lorentz vectors in an explicit covariant form. The fact that the obtained expression involves only one auxiliary vector makes it very convenient…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering…
Quantum corrections significantly influence the quantities observed in modern particle physics. The corresponding theoretical computations are usually quite lengthy which makes their automation mandatory. This review reports on the current…
The computer program `Fecom.nb' implementing the Fedosov *-product in Darboux coordinates is presented. It has been written in Mathematica 6.0 but it can be easily modified to be run in some earlier version of Mathematica. To optimize…
Version 2 of 'carlomat', a program for automatic computation of the lowest order cross sections of multiparticle reactions, is described. The substantial modifications with respect to version 1 of the program include: generation of a single…
We present the 8th Full Focal Plane simulation set (FFP8), deployed in support of the Planck 2015 results. FFP8 consists of 10 fiducial mission realizations reduced to 18144 maps, together with the most massive suite of Monte Carlo…
Rahman and Valdman (2013) introduced a new vectorized way to assemble finite element matrices. We utilize underlying vectorization concepts and extend MATLAB codes to implementation of Bogner-Fox-Schmit C1 rectangular elements in 2D. Our…
The R package calculus implements C++ optimized functions for numerical and symbolic calculus, such as the Einstein summing convention, fast computation of the Levi-Civita symbol and generalized Kronecker delta, Taylor series expansion,…
Despite outstanding performance in many tasks, language models are notoriously inclined to make factual errors in tasks requiring arithmetic computation. We address this deficiency by creating Calc-X, a collection of datasets that…