Related papers: Dirac: a command-line $\gamma$-matrix calculator
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…
An algorithm for computing the incomplete gamma function $\gamma^*(a,z)$ for real values of the parameter $a$ and negative real values of the argument $z$ is presented. The algorithm combines the use of series expansions, Poincar\'e-type…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
The types of constraints encountered in black-box and simulation-based optimization problems differ significantly from those treated in nonlinear programming. We introduce a characterization of constraints to address this situation. We…
Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only…
We describe in some detail our numerical treatment of Neuberger's lattice Dirac operator as implemented in a practical application. We discuss the improvements we have found to accelerate the numerical computations and give an estimate of…
In this paper, the Janashia-Lagvilava matrix spectral factorization algorithm, which is designed for power spectral density functions defined on the unit circle, is extended to the real line. The proposed algorithm can be used directly for…
We report on the new functionality of the open-source Mathematica package FeynCalc relevant for multiloop calculations. In particular, we focus on such tasks as topology identification by means of the Pak algorithm, search for equivalent…
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…
I give in this brief tutorial a short practical introduction to the Mathematica package SARAH. First, it is shown how an existing model file can be changed to implement a new model in SARAH. In the second part, masses, vertices and…
The nilpotent Dirac formalism has been shown, in previous publications, to generate new physical explanations for aspects of particle physics, with the additional possibility of calculating some of the parameters involved in the Standard…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
Arithmetic Kleinian groups are arithmetic lattices in PSL_2(C). We present an algorithm which, given such a group Gamma, returns a fundamental domain and a finite presentation for Gamma with a computable isomorphism.
In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$…
In perturbative calculations, e.g., in the setting of Quantum Chromodynamics (QCD) one aims at the evaluation of Feynman integrals. Here one is often faced with the problem to simplify multiple nested integrals or sums to expressions in…
Modifications of CARLOMAT, a program for automatic computation of the lowest order cross sections of multiparticle reactions, that include an abridgement of the phase space integration routine, an interface to parton density functions,…
An extremely simple, description of Karmarkar's algorithm with very few technical terms is given.
In this note, we give a geometric expression for the multiplicities of the equivariant index of a Dirac operator twisted by a line bundle.
Fisher matrices are used frequently in the analysis of combining cosmological constraints from various data sets. They encode the Gaussian uncertainties of multiple variables. They are simple to use, and I show how to get up and running…