Related papers: Package-X 2.0: A Mathematica package for the analy…
We present the PSALTer software for efficiently computing the mass and energy of the particle spectrum for any (e.g. higher-rank) tensor field theory in the Wolfram Language. The user must provide a Lagrangian density which is expanded…
TensorKit.jl is a Julia-based software package for tensor computations, especially focusing on tensors with internal symmetries. This paper introduces the design philosophy, core functionalities, and distinctive features, including how to…
We perform a complete analytical reduction of general one-loop Feynman integrals with five and six external legs for tensors up to rank R=3 and 4, respectively. An elegant formalism with extensive use of signed minors is developed for the…
We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an…
Matrix and tensor operations form the basis of a wide range of fields and applications, and in many cases constitute a substantial part of the overall computational complexity. The ability of general-purpose GPUs to speed up many of these…
We introduce SOFIA, a Mathematica package that automatizes the computation of singularities of Feynman integrals, based on new theoretical understanding of their analytic structure. Given a Feynman diagram, SOFIA generates a list of…
We use computational algorithms recently developed by us to study completely four index divergence free quadratic in Riemann tensor polynomials in GR. Some results are new and some other reproduce and/or correct known ones. The algorithms…
We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary…
We present MaRTIn, an extendable all-in-one package for calculating amplitudes up to two loops in an expansion in external momenta or using the method of infrared rearrangement. Renormalizable and non-renormalizable models can be supplied…
We report on progress for the analytical calculation of the two-loop corrections to top quark pair production at hadron colliders. For the light fermionic corrections in the gluon channel, we discuss the analytical solution for the master…
We introduce a new OpenMath content dictionary, named tensor1, containing symbols for the expression of tensor formulas. These symbols support the expression of non-Cartesian coordinates and invariant, multilinear expressions in the context…
A set of one-loop vertex and box tensor-integrals with massless internal particles has been obtained directly without any reduction method to scalar-integrals. The results with one or two massive external lines for the vertex integral and…
Nonlinear mixed effects modeling is a powerful tool when analyzing data from several entities in an experiment. In this paper, we present NLMEModeling, a package for mixed effects modeling in Wolfram Mathematica. NLMEModeling supports mixed…
Using the integration by parts method we derive a closed analytical expression for the result of the integration of an arbitrary dimensionally regulated tadpole diagram composed of a massless propagator and two massive ones, each raised…
The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This…
Using the Feynman parameter method, we have calculated in an elegant manner a set of one$-$loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and…
Evaluation of relativistic molecular integrals over exponential-type spinor orbitals require using the relativistic auxiliary functions in prolate spheroidal coordinates. They have derived recently by the author [Physical Review E 91,…
We present numerical results for massive non-planar two-loop box integrals entering heavy quark pair production at NNLO, some of which are not known analytically yet. The results have been obtained with the program SecDec 2.1, based on…
We describe two new packages ExactpAdics and ExactpAdicsII for the Magma computer algebra system for working with p-adic numbers exactly, in the sense that numbers are represented lazily to infinite p-adic precision. This has the benefits…
We present a user-friendly, open-source Wolfram Language package that automates the construction of an effective homogeneous generalized Voigt rheology for a spherically symmetric, incompressible layered body with Maxwell solid layers. It…