HypExp 2, Expanding hypergeometric functions about half-integer parameters

In this article, we describe a new algorithm for the expansion of hypergeometric functions about half-integer parameters. The implementation of this algorithm for certain classes of hypergeometric functions in the already existing Mathematica package HypExp is described. Examples of applications in Feynman diagrams with up to four loops are given.

New version program summary

Program title:HypExp 2Catalogue identifier:ADXF_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXF_v2_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.:106 401No. of bytes in distributed program, including test data, etc.:2 668 729Distribution format:tar.gzProgramming language:MathematicaComputer:Computers running MathematicaOperating system:Linux, Windows, MacRAM:Depending on the complexity of the problemSupplementary material:Library files which contain the expansion of certain hypergeometric functions around their parameters are availableClassification:4.7, 5Does the new version supersede the previous version?:YesNature of problem:Expansion of hypergeometric functions about parameters that are integer and/or half-integer valued.Solution method:New algorithm implemented in Mathematica.Reasons for new version:Expansion about half-integer parameters.Summary of revisions:Ability to expand about half-integer valued parameters added.Restrictions:The classes of hypergeometric functions with half-integer parameters that can be expanded are listed below.Additional comments:The package uses the package HPL included in the distribution.Running time:Depending on the expansion.     

Extension of HPL to complex arguments

In this paper we describe the extension of the Mathematica package HPL to treat harmonic polylogarithms of complex arguments. The harmonic polylogarithms have been introduced by Remiddi and Vermaseren [E. Remiddi, J.A.M. Vermaseren, Int. J. Modern Phys. A 15 (2000) 725, hep-ph/9905237] and have many applications in high energy particle physics.New version program summaryProgram title: HPLCatalogue identifier: ADWX_v2_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWX_v2_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.: 13 610No. of bytes in distributed program, including test data, etc.: 1 055 706Distribution format: tar.gzProgramming language: Mathematica 7/8.Computer: All computers running Mathematica.Operating system: Operating systems running Mathematica.Supplementary material: Additional “high weight” MinimalSet files available.Classification: 4.7.Catalogue identifier of previous version: ADWX_v1_0Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 222Does the new version supersede the previous version?: YesNature of problem: Computer algebraic treatment of the harmonic polylogarithms which appear in the evaluation of Feynman diagrams.Solution method: Mathematica implementation.Reasons for new version: Added treatment of complex arguments. Details in arXiv:hep-ph/0703052.Summary of revisions: Added treatment of complex arguments. Details in arXiv:hep-ph/0703052.Running time: A few seconds for each function.     

Algorithmic derivation of Dyson-Schwinger equations

We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE¹ which provides such an implementation. It derives the Dyson-Schwinger equations graphically once the interactions of the theory are specified. A few examples for the application of both the algorithm and the DoDSE package are provided.

Program summary

Program title: DoDSECatalogue identifier: AECT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECT_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.: 105 874No. of bytes in distributed program, including test data, etc.: 262 446Distribution format: tar.gzProgramming language: Mathematica 6 and higherComputer: all on which Mathematica is availableOperating system: all on which Mathematica is availableClassification: 11.1, 11.4, 11.5, 11.6Nature of problem: Derivation of Dyson-Schwinger equations for a theory with given interactions.Solution method: Implementation of an algorithm for the derivation of Dyson-Schwinger equations.Unusual features: The results can be plotted as Feynman diagrams in Mathematica.Running time: Less than a second to minutes for Dyson-Schwinger equations of higher vertex functions.     

Generating and using truly random quantum states in Mathematica

The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely Quantis quantum random number generator (QRNG), for investigating statistical properties of quantum states. The described package implements a number of functions for generating random states, which use Quantis QRNG as a source of randomness. It also provides procedures which can be used in simulations not related directly to quantum information processing.Program summaryProgram title: TRQSCatalogue identifier: AEKA_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKA_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.: 7924No. of bytes in distributed program, including test data, etc.: 88 651Distribution format: tar.gzProgramming language: Mathematica, CComputer: Requires a Quantis quantum random number generator (QRNG, http://www.idquantique.com/true-random-number-generator/products-overview.html) and supporting a recent version of MathematicaOperating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit)RAM: Case dependentClassification: 4.15Nature of problem: Generation of random density matrices.Solution method: Use of a physical quantum random number generator.Running time: Generating 100 random numbers takes about 1 second, generating 1000 random density matrices takes more than a minute.     

S@M, a mathematica implementation of the spinor-helicity formalism

In this paper we present the package S@M (Spinors@Mathematica) which implements the spinor-helicity formalism in Mathematica. The package allows the use of complex-spinor algebra along with the multi-purpose features of Mathematica. The package defines the spinor objects with their basic properties along with functions to manipulate them. It also offers the possibility of evaluating the spinorial objects numerically at every computational step. The package is therefore well suited to be used in the context of on-shell technology, in particular for the evaluation of scattering amplitudes at tree- and loop-level.

Program summary

Program title: S@MCatalogue identifier: AEBF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBF_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.: 14 404No. of bytes in distributed program, including test data, etc.: 77 536Distribution format: tar.gzProgramming language: MathematicaComputer: All computers running MathematicaOperating system: Any system running MathematicaClassification: 4.4, 5, 11.1Nature of problem: Implementation of the spinor-helicity formalismSolution method: Mathematica implementationRunning time: The notebooks provided with the package take only a few seconds to run.     

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).     

The Invar tensor package

The Invar package is introduced, a fast manipulator of generic scalar polynomial expressions formed from the Riemann tensor of a four-dimensional metric-compatible connection. The package can maximally simplify any polynomial containing tensor products of up to seven Riemann tensors within seconds. It has been implemented both in Mathematica and Maple algebraic systems.

Program summary

Program title:Invar Tensor PackageCatalogue identifier:ADZK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZK_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.: 136 240No. of bytes in distributed program, including test data, etc.:2 711 923Distribution format:tar.gzProgramming language:Mathematica and MapleComputer:Any computer running Mathematica versions 5.0 to 5.2 or Maple versions 9 and 10Operating system:Linux, Unix, Windows XPRAM:30 MbWord size:64 or 32 bitsClassification:5External routines:The Mathematica version requires the xTensor and xPerm packages. These are freely available at http://metric.iem.csic.es/Martin-Garcia/xActNature of problem:Manipulation and simplification of tensor expressions. Special attention on simplifying scalar polynomial expressions formed from the Riemann tensor on a four-dimensional metric-compatible manifold.Solution method:Algorithms of computational group theory to simplify expressions with tensors that obey permutation symmetries. Tables of syzygies of the scalar invariants of the Riemann tensor.Restrictions:The present versions do not fully address the problem of reducing differential invariants or monomials of the Riemann tensor with free indices.Running time:Less than a second to fully reduce a monomial of the Riemann tensor of degree 7 in terms of independent invariants.     

TiReX: Replica-exchange molecular dynamics using Tinker

We present a driver program for performing replica-exchange molecular dynamics simulations with the Tinker package. Parallelization is based on the Message Passing Interface, with every replica assigned to a separate process. The algorithm is not communication intensive, which makes the program suitable for running even on loosely coupled cluster systems. Particular attention is paid to the practical aspects of analyzing the program output.

Program summary

Program title: TiReXCatalogue identifier: AEEK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEK_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.: 43 385No. of bytes in distributed program, including test data, etc.: 502 262Distribution format: tar.gzProgramming language: Fortran 90/95Computer: Most UNIX machinesOperating system: LinuxHas the code been vectorized or parallelized?: parallelized with MPIClassification: 16.13External routines: TINKER version 4.2 or 5.0, built as a libraryNature of problem: Replica-exchange molecular dynamics.Solution method: Each replica is assigned to a separate process; temperatures are swapped between replicas at regular time intervals.Running time: The sample run may take up to a few minutes.     

QDENSITY—A Mathematica quantum computer simulation

This Mathematica 6.0 package is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc.

New version program summary

Program title: QDENSITY 2.0Catalogue identifier: ADXH_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v2_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 055No. of bytes in distributed program, including test data, etc.: 227 540Distribution format: tar.gzProgramming language: Mathematica 6.0Operating system: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4Catalogue identifier of previous version: ADXH_v1_0Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 914Classification: 4.15Does the new version supersede the previous version?: Offers an alternative, more up to date, implementationNature of problem: Analysis and design of quantum circuits, quantum algorithms and quantum clusters.Solution method: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are explained in detail. A tutorial, Tutorial.nb is also enclosed.Reasons for new version: The package has been updated to make it fully compatible with Mathematica 6.0Summary of revisions: The package has been updated to make it fully compatible with Mathematica 6.0Running time: Most examples included in the package, e.g., the tutorial, Shor's examples, Teleportation examples and Grover's search, run in less than a minute on a Pentium 4 processor (2.6 GHz). The running time for a quantum computation depends crucially on the number of qubits employed.     

A completely open source based computing system for computer generation of Fourier holograms

Computer generated holograms are usually generated using commercial software like MATLAB, MATHCAD, Mathematica, etc. This work is an approach in doing the same using freely distributed open source packages and Operating System. A Fourier hologram is generated using this method and tested for simulated and optical reconstruction. The reconstructed images are in good agreement with the objects chosen. The significance of using such a system is also discussed.

Program summary

Program title: FHOLOCatalogue identifier: AEDS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDS_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 336No. of bytes in distributed program, including test data, etc.: 4 294 872Distribution format: tar.gzProgramming language: C++Computer: any X86 micro computerOperating system: Linux (Debian Etch)RAM: 512 MBClassification: 18Nature of problem: To generate a Fourier Hologram in micro computer only by using open source operating system and packages.Running time: Depends on the matrix size. 10 sec for a matrix of size 256×256.     

A program to compute exact hydrogenic radial integrals and Einstein coefficients

An exact expression for the dipole radial integral of hydrogen has been given by Gordon [Ann. Phys. 2 (1929) 1031]. It contains two hypergeometric functions F(a,b;c;x), which are difficult to calculate directly, when the (negative) integers a, b are large, as in the case of high Rydberg states of hydrogenic ions. We have derived a simple method [D. Hoang-Binh, Astron. Astrophys. 238 (1990) 449], using a recurrence relation to calculate exactly F, starting from two initial values, which are very easy to compute. We present here a numerical code using this method. The code computes exact hydrogenic radial integrals, oscillator strengths, Einstein coefficients, and lifetimes, for principal quantum numbers up to 1000.

Program summary

Program title: ba5.2Catalogue identifier: ADUU_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUU_v2_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.: 1400No. of bytes in distributed program, including test data, etc.: 11 737Distribution format: tar.gzProgramming language: Fortran 77Computer: PC, iMacOperating system: Linux/Unix, MacOS 9.0RAM: Less than 1 MBClassification: 2, 2.2Catalogue identifier of previous version: ADUU_v1_0Journal reference of previous version: Comput. Phys. Comm. 166 (2005) 191Does the new version supersede the previous version?: YesNature of problem: Exact calculation of atomic data.Solution method: Use of a recurrence relation to compute hypergeometric functions.Reasons for new version: This new version computes additional important related data, namely, the total Einstein coefficients, and radiative lifetimes.Summary of revisions: Values of the total Einstein transition probability from an upper level n to a lower level n^′ are computed, as well as the radiative lifetime of a level n.Running time: About 2 seconds     

Milne, a routine for the numerical solution of Milne's problem

The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct.

Program summary

Program title: MilneCatalogue identifier: AEGS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_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.: 701No. of bytes in distributed program, including test data, etc.: 6845Distribution format: tar.gzProgramming language: Fortran 77Computer: PC under Linux or WindowsOperating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XPClassification: 4.11, 21.1, 21.2Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature.Running time: The test included in the distribution takes a few seconds to run.     

Solution of few-body problems with the stochastic variational method II: Two-dimensional systems

A computational approach is presented for efficient solution of two-dimensional few-body problems, such as quantum dots or excitonic complexes, using the stochastic variational method. The computer program can be used to calculate the energies and wave functions of various two-dimensional systems.

Program summary

Program title: svm-2dCatalogue identifier: AEBE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBE_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.: 5091No. of bytes in distributed program, including test data, etc.: 130 963Distribution format: tar.gzProgramming language: Fortran 90Computer: The program should work on any system with a Fortran 90 compilerOperating system: The program should work on any system with a Fortran 90 compilerClassification: 7.3Nature of problem: Variational calculation of energies and wave functions using Correlated Gaussian basis.Solution method: Two-dimensional few-electron problems are solved by the variational method. The ground state wave function is expanded into Correlated Gaussian basis functions and the parameters of the basis states are optimized by a stochastic selection procedure. Accurate results can be obtained for 2-6 electron systems.Running time: A couple of hours for a typical system.     

Symbolic computation of the Hartree-Fock energy from a chiral EFT three-nucleon interaction at NLO

We present the first of a two-part Mathematica notebook collection that implements a symbolic approach for the application of the density matrix expansion (DME) to the Hartree-Fock (HF) energy from a chiral effective field theory (EFT) three-nucleon interaction at N²LO. The final output from the notebooks is a Skyrme-like energy density functional that provides a quasi-local approximation to the non-local HF energy. In this paper, we discuss the derivation of the HF energy and its simplification in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix. Furthermore, a set of steps is described and illustrated on how to extend the approach to other three-nucleon interactions.

Program summary

Program title: SymbHFNNNCatalogue identifier: AEGC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGC_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.: 96 666No. of bytes in distributed program, including test data, etc.: 378 083Distribution format: tar.gzProgramming language: Mathematica 7.1Computer: Any computer running Mathematica 6.0 and later versionsOperating system: Windows Xp, Linux/UnixRAM: 256 MbClassification: 5, 17.16, 17.22Nature of problem: The calculation of the HF energy from the chiral EFT three-nucleon interaction at N²LO involves tremendous spin-isospin algebra. The problem is compounded by the need to eventually obtain a quasi-local approximation to the HF energy, which requires the HF energy to be expressed in terms of scalar/vector-isoscalar/isovector parts of the one-body density matrix. The Mathematica notebooks discussed in this paper solve the latter issue.Solution method: The HF energy from the chiral EFT three-nucleon interaction at N²LO is cast into a form suitable for an automatic simplification of the spin-isospin traces. Several Mathematica functions and symbolic manipulation techniques are used to obtain the result in terms of the scalar/vector-isoscalar/isovector parts of the one-body density matrix.Running time: Several hours     

SMMP v. 3.0—Simulating proteins and protein interactions in Python and Fortran

We describe a revised and updated version of the program package SMMP. SMMP is an open-source FORTRAN package for molecular simulation of proteins within the standard geometry model. It is designed as a simple and inexpensive tool for researchers and students to become familiar with protein simulation techniques. SMMP 3.0 sports a revised API increasing its flexibility, an implementation of the Lund force field, multi-molecule simulations, a parallel implementation of the energy function, Python bindings, and more.

Program summary

Title of program:SMMPCatalogue identifier:ADOJ_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADOJ_v3_0.htmlProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlProgramming language used:FORTRAN, PythonNo. of lines in distributed program, including test data, etc.:52 105No. of bytes in distributed program, including test data, etc.:599 150Distribution format:tar.gzComputer:Platform independentOperating system:OS independentRAM:2 MbytesClassification:3Does the new version supersede the previous version?:YesNature of problem:Molecular mechanics computations and Monte Carlo simulation of proteins.Solution method:Utilizes ECEPP2/3, FLEX, and Lund potentials. Includes Monte Carlo simulation algorithms for canonical, as well as for generalized ensembles.Reasons for new version:API changes and increased functionality.Summary of revisions:Added Lund potential; parameters used in subroutines are now passed as arguments; multi-molecule simulations; parallelized energy calculation for ECEPP; Python bindings.Restrictions:The consumed CPU time increases with the size of protein molecule.Running time:Depends on the size of the simulated molecule.     

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.     

Symbolic computation of analytic approximate solutions for nonlinear differential equations with initial conditions

The Adomian decomposition method (ADM) is one of the most effective methods for constructing analytic approximate solutions of nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, and the two-step Adomian decomposition method (TSADM) combined with the Padé technique, a new algorithm is proposed to construct accurate analytic approximations of nonlinear differential equations with initial conditions. Furthermore, a MAPLE package is developed, which is user-friendly and efficient. One only needs to input a system, initial conditions and several necessary parameters, then our package will automatically deliver analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the validity of the package. Our program provides a helpful and easy-to-use tool in science and engineering to deal with initial value problems.Program summaryProgram title: NAPACatalogue identifier: AEJZ_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEJZ_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.: 4060No. of bytes in distributed program, including test data, etc.: 113 498Distribution format: tar.gzProgramming language: MAPLE R13Computer: PCOperating system: Windows XP/7RAM: 2 GbytesClassification: 4.3Nature of problem: Solve nonlinear differential equations with initial conditions.Solution method: Adomian decomposition method and Padé technique.Running time: Seconds at most in routine uses of the program. Special tasks may take up to some minutes.     

LIBERI: Library for numerical evaluation of electron-repulsion integrals

We provide a C library, called LIBERI, for numerical evaluation of four-center electron repulsion integrals, based on successive reduction of integral dimension by using Fourier transforms. LIBERI enables us to compute the integrals for numerically defined basis functions within ¹⁰−5 Hartree accuracy as well as their derivatives with respect to the atomic nuclear positions. Damping of the Coulomb interaction can also be imposed to take account of screening effect.

Program summary

Program title: LIBERICatalogue identifier: AEGG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGG_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.: 44 091No. of bytes in distributed program, including test data, etc.: 1 692 085Distribution format: tar.gzProgramming language: CComputer: allOperating system: any Unix-like systemRAM: 5-10 MbClassification: 7.4External routines: Lapack (http://www.netlib.org/lapack/), Blas (http://www.netlib.org/blas/), FFTW3 (http://www.fftw.org/)Nature of problem: Numerical evaluation of four-center electron-repulsion integrals.Solution method: Four-center electron-repulsion integrals are computed for given basis function set, based on successive reduction of integral dimension using Fourier transform.Running time: 0.5 sec for the demo program supplied with the package.     

HidSecSOFTSUSY: Incorporating effects from hidden sectors in the numerical computation of the MSSM spectrum

SOFTSUSY is a software designed to solve the RG equations of the MSSM and compute its low energy spectrum. HidSecSOFTSUSY is an extension of the SOFTSUSY package which modifies the beta functions to include contributions from light dynamic fields in the hidden sector.

Program summary

Program title: HidSecSOFTSUSYCatalogue identifier: AEHP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHP_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.: 4167No. of bytes in distributed program, including test data, etc.: 141 411Distribution format: tar.gzProgramming language: C++, FortranComputer: Personal computerOperating system: Tested on GNU/LinuxWord size: 32 bitsClassification: 11.6External routines: Requires an installed version of SOFTSUSY (http://projects.hepforge.org/softsusy/)Nature of problem: Calculating supersymmetric particle spectrum and mixing parameters while incorporating dynamic modes from the hidden sector into the renormalization group equations. The solution to the equations must be consistent with a high-scale boundary condition on supersymmetry breaking parameters, as well as a weak-scale boundary condition on gauge couplings, Yukawa couplings and the Higgs potential parameters.Solution method: Nested iterative algorithm.Running time: A few seconds per parameter point.