A recursive method to calculate UV-divergent parts at one-loop level in dimensional regularization

A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which involve no other momentum scales except the loop momentum itself. The method can be easily implemented in any symbolic computer language, and a implementation in Mathematica is ready to use.Program summaryProgram title: UVPartCatalogue identifier: AELY_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELY_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 26 361No. of bytes in distributed program, including test data, etc.: 412 084Distribution format: tar.gzProgramming language: MathematicaComputer: Any computer where the Mathematica is running.Operating system: Any capable of running Mathematica.Classification: 11.1External routines: FeynCalc (http://www.feyncalc.org/), FeynArts (http://www.feynarts.de/)Nature of problem: To get the UV-divergent part of any one-loop expression.Solution method: UVPart is a Mathematica package where the recursive method has been implemented.Running time: In general it is below one second.     

Resolution of singularities for multi-loop integrals

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program.

Program summary

Program title: sector_decompositionCatalogue identifier: AEAG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 47 506No. of bytes in distributed program, including test data, etc.: 328 485Distribution format: tar.gzProgramming language: C++Computer: allOperating system: UnixRAM: Depending on the complexity of the problemClassification: 4.4External routines: GiNaC, available from http://www.ginac.de, GNU scientific library, available from http://www.gnu.org/software/gslNature of problem: Computation of divergent multi-loop integrals.Solution method: Sector decomposition.Restrictions: Only limited by the available memory and CPU time.Running time: Depending on the complexity of the problem.     

Monte Carlo event generator for black hole production and decay in proton-proton collisions - QBH version 1.02

We describe the Monte Carlo event generator for black hole production and decay in proton-proton collisions - QBH version 1.02. The generator implements a model for quantum black hole production and decay based on the conservation of local gauge symmetries and democratic decays. The code in written entirely in C++ and interfaces to the PYTHIA 8 Monte Carlo code for fragmentation and decays.

Program summary

Program title: QBHCatalogue identifier: AEGU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 10 048No. of bytes in distributed program, including test data, etc.: 118 420Distribution format: tar.gzProgramming language: C++Computer: x86Operating system: Scientific Linux, Mac OS XRAM: 1 GBClassification: 11.6External routines: PYTHIA 8130 (http://home.thep.lu.se/~torbjorn/pythiaaux/present.html) and LHAPDF (http://projects.hepforge.org/lhapdf/)Nature of problem: Simulate black hole production and decay in proton-proton collision.Solution method: Monte Carlo simulation using importance sampling.Running time: Eight events per second.     

JuNoLo - Jülich nonlocal code for parallel post-processing evaluation of vdW-DF correlation energy

Nowadays the state of the art Density Functional Theory (DFT) codes are based on local (LDA) or semilocal (GGA) energy functionals. Recently the theory of a truly nonlocal energy functional has been developed. It has been used mostly as a post-DFT calculation approach, i.e. by applying the functional to the charge density calculated using any standard DFT code, thus obtaining a new improved value for the total energy of the system. Nonlocal calculation is computationally quite expensive and scales as N² where N is the number of points in which the density is defined, and a massively parallel calculation is welcome for a wider applicability of the new approach. In this article we present a code which accomplishes this goal.

Program summary

Program title: JuNoLoCatalogue identifier: AEFM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 176 980No. of bytes in distributed program, including test data, etc.: 2 126 072Distribution format: tar.gzProgramming language: Fortran 90Computer: any architecture with a Fortran 90 compilerOperating system: Linux, AIXHas the code been vectorised or parallelized?: Yes, from 1 to 65536 processors may be used.RAM: depends strongly on the problem's size.Classification: 7.3External routines:• FFTW (http://www.tw.org/)• MPI (http://www.mcs.anl.gov/research/projects/mpich2/ or http://www.lam-mpi.org/)Nature of problem: Obtaining the value of the nonlocal vdW-DF energy based on the charge density distribution obtained from some Density Functional Theory code.Solution method: Numerical calculation of the double sum is implemented in a parallel F90 code. Calculation of this sum yields the required nonlocal vdW-DF energy.Unusual features: Binds to virtually any DFT program.Additional comments: Excellent parallelization features.Running time: Depends strongly on the size of the problem and the number of CPUs used.     

HFOLD - A program package for calculating two-body MSSM Higgs decays at full one-loop level

HFOLD (Higgs Full One Loop Decays) is a Fortran program package for calculating all MSSM Higgs two-body decay widths and the corresponding branching ratios at full one-loop level. The package is done in the SUSY Parameter Analysis convention and supports the SUSY Les Houches Accord input and output format.

Program summary

Program title: HFOLDCatalogue identifier: AEJG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 340 621No. of bytes in distributed program, including test data, etc.: 1 760 051Distribution format: tar.gzProgramming language: Fortran 77Computer: Workstation, PCOperating system: LinuxRAM: 524 288 000 BytesClassification: 11.1External routines: LoopTools 2.2 (http://www.feynarts.de/looptools/), SLHALib 2.2 (http://www.feynarts.de/slha/). The LoopTools code is included in the distribution package.Nature of problem: A future high-energy e⁺e⁻ linear collider will be the best environment for the precise measurements of masses, cross sections, branching ratios, etc. Experimental accuracies are expected at the per-cent down to the per-mile level. These must be matched from the theoretical side. Therefore higher order calculations are mandatory.Solution method: This program package calculates all MSSM Higgs two-body decay widths and the corresponding branching ratios at full one-loop level. The renormalization is done in the DR scheme following the SUSY Parameter Analysis convention. The program supports the SUSY Les Houches Accord input and output format.Running time: The example provided takes only a few seconds to run.     

Real-time Java simulations of multiple interference dielectric filters

An interactive Java applet for real-time simulation and visualization of the transmittance properties of multiple interference dielectric filters is presented. The most commonly used interference filters as well as the state-of-the-art ones are embedded in this platform-independent applet which can serve research and education purposes. The Transmittance applet can be freely downloaded from the site http://cpc.cs.qub.ac.uk.

Program summary

Program title: TransmittanceCatalogue identifier: AEBQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5778No. of bytes in distributed program, including test data, etc.: 90 474Distribution format: tar.gzProgramming language: JavaComputer: Developed on PC-Pentium platformOperating system: Any Java-enabled OS. Applet was tested on Windows ME, XP, Sun Solaris, Mac OSRAM: VariableClassification: 18Nature of problem: Sophisticated wavelength selective multiple interference filters can include some tens or even hundreds of dielectric layers. The spectral response of such a stack is not obvious. On the other hand, there is a strong demand from application designers and students to get a quick insight into the properties of a given filter.Solution method: A Java applet was developed for the computation and the visualization of the transmittance of multilayer interference filters. It is simple to use and the embedded filter library can serve educational purposes. Also, its ability to handle complex structures will be appreciated as a useful research and development tool.Running time: Real-time simulations     

Vscape V1.1.0. An interactive tool for metastable vacua

Vscape is an interactive tool for studying the one-loop effective potential of an ungauged supersymmetric model of chiral multiplets. The program allows the user to define a supersymmetric model by specifying the superpotential. The F-terms and the scalar and fermionic mass matrices are calculated symbolically. The program then allows you to search numerically for (meta)stable minima of the one-loop effective potential. Additional commands enable you to further study specific minima, by, e.g., computing the mass spectrum for those vacua. Vscape combines the flexibility of symbolic software, with the speed of a numerical package.

Program summary

Program title:Vscape 1.1.1Catalogue identifier: ADZW_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZW_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 80 507No. of bytes in distributed program, including test data, etc.: 6 708 938Distribution format: tar.gzProgramming language: C++Computer: Pentium 4 PC Computers: need (GNU) C++ compiler, Linux standard GNU installation (./configure; make; make install). A precompiled Windows XP version is included in the distribution packageOperating system: Linux, Windows XP using cygwinRAM: 10 MBWord size: 32 bitsClassification: 11.6External routines: GSL (http://www.gnu.org/software/gsl/), CLN (http://www.ginac.de/CLN/), GiNaC (http://directory.fsf.org/GiNaC.html)Nature of problem:Vscape is an interactive tool for studying the one-loop effective potential of an ungauged supersymmetric model of chiral multiplets. The program allows the user to define a supersymmetric model by specifying the superpotential. The F-terms and the scalar and fermionic mass matrices are calculated symbolically. The program then allows you to search numerically for (meta)stable minima of the one-loop effective potential. Additional commands enable you to further study specific minima, by, e.g., computing the mass spectrum for those vacua. Vscape combines the flexibility of symbolic software with the speed of a numerical package.Solution method: Coleman-Weinberg potential is computed using numerical matrix diagonalization. Minima of the one-loop effective potential are found using the Nelder and Mead simplex algorithm. The one-loop effective potential can be studied using numerical differentiation. Symbolic users interface implemented using flex and bison.Restrictions:N=1 supersymmetric chiral models onlyUnusual features: GiNaC (+CLN), GSL, ReadLib (not essential)Running time: Interactive users interface. Most commands execute in a few ms. Computationally intensive commands execute in order of minutes, depending on the complexity of the user defined model.     

Parallel FFT-based Poisson solver for isolated three-dimensional systems

We describe an implementation to solve Poisson?s equation for an isolated system on a unigrid mesh using FFTs. The method solves the equation globally on mesh blocks distributed across multiple processes on a distributed-memory parallel computer. Test results to demonstrate the convergence and scaling properties of the implementation are presented. The solver is offered to interested users as the library PSPFFT.

Program summary

Program title: PSPFFTCatalogue identifier: AEJK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 110 243No. of bytes in distributed program, including test data, etc.: 16 332 181Distribution format: tar.gzProgramming language: Fortran 95Computer: Any architecture with a Fortran 95 compiler, distributed memory clustersOperating system: Linux, UnixHas the code been vectorized or parallelized?: Yes, using MPI. An arbitrary number of processors may be used (subject to some constraints). The program has been tested on from 1 up to ∼ 13 000 processors. RAM: Depends on the problem size, approximately 170 MBytes for 48³ cells per process.Classification: 4.3, 6.5External routines: MPI (http://www.mcs.anl.gov/mpi/), FFTW (http://www.fftw.org), Silo (https://wci.llnl.gov/codes/silo/) (only necessary for running test problem).Nature of problem: Solving Poisson?s equation globally on unigrid mesh distributed across multiple processes on distributed memory system.Solution method: Numerical solution using multidimensional discrete Fourier Transform in a parallel Fortran 95 code.Unusual features: This code can be compiled as a library to be readily linked and used as a blackbox Poisson solver with other codes.Running time: Depends on the size of the problem, but typically less than 1 second per solve.     

Motion4D - A library for lightrays and timelike worldlines in the theory of relativity

The Motion4D-library solves the geodesic equation as well as the parallel- and Fermi-Walker-transport in four-dimensional Lorentzian spacetimes numerically. Initial conditions are given with respect to natural local tetrads which are adapted to the symmetries or the coordinates of the spacetime. Beside some already implemented metrics like the Schwarzschild and Kerr metric, the object oriented structure of the library permits to implement other metrics or integrators in a straight forward manner.

Program summary

Program title: Motion4D-libraryCatalogue identifier: AEEX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEX_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 150 425No. of bytes in distributed program, including test data, etc.: 5 139 407Distribution format: tar.gzProgramming language: C++Computer: All platforms with a C++ compilerOperating system: Linux, Unix, WindowsRAM: 39 MBytesClassification: 1.5External routines: Gnu Scientific Library (GSL) (http://www.gnu.org/software/gsl/)Nature of problem: Solve geodesic equation, parallel and Fermi-Walker transport in four-dimensional Lorentzian spacetimes.Solution method: Integration of ordinary differential equationsRunning time: The test runs provided with the distribution require only a few seconds to run.     

SecDec: A general program for sector decomposition

We present a program for the numerical evaluation of multi-dimensional polynomial parameter integrals. Singularities regulated by dimensional regularisation are extracted using iterated sector decomposition. The program evaluates the coefficients of a Laurent series in the regularisation parameter. It can be applied to multi-loop integrals in Euclidean space as well as other parametric integrals, e.g. phase space integrals.

Program summary

Program title: SecDecCatalogue identifier: AEIR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 57 617No. of bytes in distributed program, including test data, etc.: 895 550Distribution format: tar.gzProgramming language: Wolfram Mathematica, perl, FortranComputer: From a single PC to a cluster, depending on the problemOperating system: Unix, LinuxRAM: Depends on the complexity of the problemClassification: 4.4, 5, 11.1Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories, e.g. multi-loop Feynman integrals, Wilson loops, phase space integrals.Solution method: Algebraic extraction of singularities in dimensional regularisation using iterated sector decomposition. This leads to a Laurent series in the dimensional regularisation parameter ε, where the coefficients are finite integrals over the unit-hypercube. Those integrals are evaluated numerically by Monte Carlo integration.Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. Multi-scale integrals can only be evaluated at Euclidean points.Running time: Between a few minutes and several days, depending on the complexity of the problem.     

HRMC: Hybrid Reverse Monte Carlo method with silicon and carbon potentials

Fortran 77 code is presented for a hybrid method of the Metropolis Monte Carlo (MMC) and Reverse Monte Carlo (RMC) for the simulation of amorphous silicon and carbon structures. In additional to the usual constraints of the pair correlation functions and average coordination, the code also incorporates an optional energy constraint. This energy constraint is in the form of either the Environment Dependent Interatomic Potential (applicable to silicon and carbon) and the original and modified Stillinger-Weber potentials (applicable to silicon). The code also allows porous systems to be modeled via a constraint on porosity and internal surface area using a novel restriction on the available simulation volume.

Program summary

Program title: HRMC version 1.0Catalogue identifier: AEAO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 200 894No. of bytes in distributed program, including test data, etc.: 907 557Distribution format: tar.gzProgramming language: FORTRAN 77Computer: Any computer capable of running executables produced by the g77 Fortran compilerOperating system: Unix, WindowsRAM: Depends on the type of empirical potential use, number of atoms and which constraints are employedClassification: 7.7Nature of problem: Atomic modeling using empirical potentials and experimental dataSolution method: Monte CarloAdditional comments: The code is not standard FORTRAN 77 but includes some additional features and therefore generates errors when compiled using the Nag95 compiler. It does compile successfully with the GNU g77 compiler (http://www.gnu.org/software/fortran/fortran.html).Running time: Depends on the type of empirical potential use, number of atoms and which constraints are employed. The test included in the distribution took 37 minutes on a DEC Alpha PC.     

Solving surface structures from normal incidence X-ray standing wave data

A program is provided to determine structural parameters of atoms in or adsorbed on surfaces by refinement of atomistic models towards experimentally determined data generated by the normal incidence X-ray standing wave (NIXSW) technique. The method employs a combination of Differential Evolution Genetic Algorithms and Steepest Descent Line Minimisations to provide a fast, reliable and user friendly tool for experimentalists to interpret complex multidimensional NIXSW data sets.

Program summary

Program title: NIXSW Planewave SolverCatalogue identifier: ADZE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 16 874No. of bytes in distributed program, including test data, etc.: 1 631 874Distribution format: tar.gzProgramming language: Borland C++ Builder 5Computer: Any Windows CompatibleOperating system: Windows 2000 and XPRAM: <10 MBClassification: 7.4Nature of problem: Using NIXSW experimental data to calculate atomic positions of adsorbates.Restrictions: Data from substrates must have cubic, tetragonal or orthorhombic crystal structures i.e. with 90° between conventional cell axes.Running time: Seconds-minutes dependant on the number of plane waves and the number of atomic sites.     

QCDMAPT: Program package for Analytic approach to QCD

A program package, which facilitates computations in the framework of Analytic approach to QCD, is developed and described in detail. The package includes both the calculated explicit expressions for relevant spectral functions up to the four-loop level and the subroutines for necessary integrals.

Program summary

Program title: QCDMAPTCatalogue identifier: AEGP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2579No. of bytes in distributed program, including test data, etc.: 180 052Distribution format: tar.gzProgramming language: Maple 9 and higherComputer: Any which supports Maple 9Operating system: Any which supports Maple 9Classification: 11.1, 11.5, 11.6Nature of problem: Subroutines helping computations within Analytic approach to QCD.Solution method: A program package for Maple is provided. It includes both the explicit expressions for relevant spectral functions and the subroutines for basic integrals used in the framework of Analytic approach to QCD.Running time: Template program running time is about a minute (depends on CPU).     

MDVRY: a polarizable classical molecular dynamics package for biomolecules

The MDVRY classical molecular dynamics package is presented for the study of biomolecules in the gas and liquid phase. Electrostatic polarization has been implemented in the formalism of point induced dipoles following the model of Thole. Two schemes have been implemented for the calculation of induced dipoles, i.e. resolution of the self-consistent equations and a ‘Car-Parrinello’ dynamical approach. In this latter, the induced dipoles are calculated at each time step of the dynamics through the dynamics of additional degrees of freedom associated with the dipoles. This method saves computer time and allows to study polarized solvated proteins at a very low CPU cost. The program is written in C-language and runs on LINUX machines. A detailed manual of the code is given. The main features of the package are illustrated taking on examples of proteins in the gas phase or immersed in liquid water.

Program summary

Program title: MDVRYCatalogue identifier: AEBY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBY_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 39 156No. of bytes in distributed program, including test data, etc.: 277 197Distribution format: tar.bz2Programming language: CComputer: Linux machines with FFTW Fourier Transform package installedOperating system: Linux machines, SUSE & RedHat distributionsClassification: 3, 16.13, 23External routines: FFTW (http://www.fftw.org/)Nature of problem: Molecular Dynamics Software package.Solution method: Velocity Verlet algorithm. The implemented force field is composed of intra-molecular interactions and inter-molecular interactions (electrostatics, polarization, van der Waals). Polarization is accounted through induced point dipoles at each atomic site. Supplementary degrees of freedom are associated to the induced dipoles so that a modified Hamiltonian of the dynamics is written. This allows to calculate the induced dipoles with a very fast ‘Car-Parrinello’ type of dynamics.Running time: The test run provided takes approximately 6 minutes to run.     

GeodesicViewer - A tool for exploring geodesics in the theory of relativity

The GeodesicViewer realizes exocentric two- and three-dimensional illustrations of lightlike and timelike geodesics in the general theory of relativity. By means of an intuitive graphical user interface, all parameters of a spacetime as well as the initial conditions of the geodesics can be modified interactively. This makes the GeodesicViewer a useful instrument for the exploration of geodesics in four-dimensional Lorentzian spacetimes.

Program summary

Program title: GeodesicViewerCatalogue identifier: AEFP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 168 868No. of bytes in distributed program, including test data, etc.: 6 076 202Distribution format: tar.gzProgramming language: C++, Qt, Qwt, OpenGLComputer: All platforms with a C++ compiler, Qt, Qwt, OpenGLOperating system: Linux, Mac OS XRAM: 24 MbytesClassification: 1.5External routines:

•

Gnu Scientific Library (GSL) (http://www.gnu.org/software/gsl/)

•

Motion4D (included in the package). The Motion4D library can also be downloaded from CPC. Catalogue identifier: AEEX

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Qt (http://qt.nokia.com/downloads)

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Qwt (http://qwt.sourceforge.net/)

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OpenGL (http://www.opengl.org/)

Nature of problem: Illustrate geodesics in four-dimensional Lorentzian spacetimes.Solution method: Integration of ordinary differential equations. 3D-Rendering via OpenGL.Running time: Interactive. The examples given take milliseconds.