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.     

HPL, a Mathematica implementation of the harmonic polylogarithms

In this paper, we present an implementation of the harmonic polylogarithm of Remiddi and Vermaseren [E. Remiddi, J.A.M. Vermaseren, Int. J. Modern Phys. A 15 (2000) 725, hep-ph/9905237] for Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation. The analytic continuation has been treated carefully, allowing the user to keep the control over the definition of the sign of the imaginary parts. Many options enables the user to adapt the behavior of the package to his specific problem.

Program summary

Program title: HPLCatalogue identifier:ADWXProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWXProgram obtained from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneProgramming language: MathematicaNo. of lines in distributed program, including test data, etc.:13 310No. of bytes in distributed program, including test data, etc.: 1 990 584Distribution format: tar.gzComputer:all computers running MathematicaOperating systems:operating systems running MathematicaNature of problem: Computer algebraic treatment of the harmonic polylogarithms which appear in the evaluation of Feynman diagramsSolution method: Mathematica implementation     

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.     

Calculation of effective conductivity of 2D and 3D composite materials with anisotropic constituents and different inclusion shapes in Mathematica

The study of the effective properties of composite materials with anisotropic constituents and different inclusion shapes has motivated the development of the Mathematica 6.0 package “CompositeMaterials”. This package can be used to calculate the effective anisotropic conductivity tensor of two-phase composites. Any fiber cross section, even percolating ones, can be studied in the 2D composites. “Rectangular Prism” and “Ellipsoidal” inclusion shapes with arbitrary orientations can be investigated in the 3D composites. This package combines the Asymptotic Homogenization Method and the Finite Element Method in order to obtain the effective conductivity tensor. The commands and options of the package are illustrated with two sample applications for two- and three-dimensional composites.

Program summary

Program title:CompositeMaterialsCatalogue identifier:AEAU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAU_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.:132 183No. of bytes in distributed program, including test data, etc.:1 334 908Distribution format:tar.gzProgramming language:Mathematica 6.0Computer:Any that can run Mathematica 6.0 and where the open-source free C-programs Triangle (http://www.cs.cmu.edu/~quake/triangle.html) and TetGen (http://tetgen.berlios.de/) can be compiled and executed. Tested in Intel Pentium computers.Operating system:Any that can run Mathematica 6.0 and where the open-source free C-programs Triangle (http://www.cs.cmu.edu/~quake/triangle.html) and TetGen (http://tetgen.berlios.de/) can be compiled and executed. Tested in Windows XP.RAM:Small two-dimensional calculations require less than 100 MB. Large three-dimensional calculations require 500 MB or more.Classification:7.9External routines:One Mathematica Add-on and two external programs: The free Mathematica Add-On IMS (http://www.imtek.uni-freiburg.de/simulation/Mathematica/IMSweb/), The open-source free C-program Triangle (http://www.cs.cmu.edu/~quake/triangle.html). The open-source free C-program TetGen (http://tetgen.berlios.de/). The distribution file contains Windows executables for Triangle and TetGen.Nature of problem:The calculation of effective thermal conductivity tensor for two-dimensional and three-dimensional composite materials with anisotropic constituents and different inclusion shapes.Solution method:Asymptotic Homogenization Method, with the Cell Problems solved with Finite Element Method.Unusual features:Different inclusion shapes can be easily created. The constituents can be anisotropic. The intermediate stages and the final results can be graphed and analyzed with all the power of Mathematica 6.0. The use of the external meshing programs Triangle and TetGen is totally transparent for the end user. A typical calculation requires the use of only four special commands that follow standard Mathematica syntax.Additional comments:The executable binary files for Triangle and TetGen must be accessible from the directory specified by Mathematica's variable $HomeDirectory. The IMS add-on and the CompositeMaterials package, which is the package presented in this work, must be installed in the directory specified by Mathematica's variable $BaseDirectory or in the variable $UserBaseDirectory. The 2D calculations of Composite Materials will run successfully in Mathematica 5.2 and 6.0 but for the 3D calculations it is necessary to use Mathematica 6.0 or higher.Running time:Simple two-dimensional calculations can be done in less than a minute. Complex three-dimensional calculations can take an hour or more.     

Lambda: A Mathematica package for operator product expansions in vertex algebras

We give an introduction to the Mathematica package Lambda, designed for calculating λ-brackets in both vertex algebras, and in SUSY vertex algebras. This is equivalent to calculating operator product expansions in two-dimensional conformal field theory. The syntax of λ-brackets is reviewed, and some simple examples are shown, both in component notation, and in N=1 superfield notation.

Program summary

Program title: LambdaCatalogue identifier: AEHF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHF_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenseNo. of lines in distributed program, including test data, etc.: 18 087No. of bytes in distributed program, including test data, etc.: 131 812Distribution format: tar.gzProgramming language: MathematicaComputer: See specifications for running Mathematica V7 or above.Operating system: See specifications for running Mathematica V7 or above.RAM: Varies greatly depending on calculation to be performed.Classification: 4.2, 5, 11.1.Nature of problem: Calculate operator product expansions (OPEs) of composite fields in 2d conformal field theory.Solution method: Implementation of the algebraic formulation of OPEs given by vertex algebras, and especially by λ-brackets.Running time: Varies greatly depending on calculation requested. The example notebook provided takes about 3 s to run.     

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.     

GeM software package for computation of symmetries and conservation laws of differential equations

We present a recently developed Maple-based “GeM” software package for automated symmetry and conservation law analysis of systems of partial and ordinary differential equations (DE). The package contains a collection of powerful easy-to-use routines for mathematicians and applied researchers. A standard program that employs “GeM” routines for symmetry, adjoint symmetry or conservation law analysis of any given DE system occupies several lines of Maple code, and produces output in the canonical form. Classification of symmetries and conservation laws with respect to constitutive functions and parameters present in the given DE system is implemented. The “GeM” package is being successfully used in ongoing research. Run examples include classical and new results.

Program summary

Title of program: GeMCatalogue identifier: ADYK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYK_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputers: PC-compatible running Maple on MS Windows or Linux; SUN systems running Maple for Unix on OS SolarisOperating systems under which the program has been tested: Windows 2000, Windows XP, Linux, SolarisProgramming language used: Maple 9.5Memory required to execute with typical data: below 100 MegabytesNo. of lines in distributed program, including test data, etc.: 4939No. of bytes in distributed program, including test data, etc.: 166 906Distribution format: tar.gzNature of physical problem: Any physical model containing linear or nonlinear partial or ordinary differential equations.Method of solution: Symbolic computation of Lie, higher and approximate symmetries by Lie's algorithm. Symbolic computation of conservation laws and adjoint symmetries by using multipliers and Euler operator properties. High performance is achieved by using an efficient representation of the system under consideration and resulting symmetry/conservation law determining equations: all dependent variables and derivatives are represented as symbols rather than functions or expressions.Restrictions on the complexity of the problem: The GeM module routines are normally able to handle ODE/PDE systems of high orders (up to order seven and possibly higher), depending on the nature of the problem. Classification of symmetries/conservation laws with respect to one or more arbitrary constitutive functions of one or two arguments is normally accomplished successfully.Typical running time: 1-20 seconds for problems that do not involve classification; 5-1000 seconds for problems that involve classification, depending on complexity.     

xPerm: fast index canonicalization for tensor computer algebra

We present a very fast implementation of the Butler-Portugal algorithm for index canonicalization with respect to permutation symmetries. It is called xPerm, and has been written as a combination of a Mathematica package and a C subroutine. The latter performs the most demanding parts of the computations and can be linked from any other program or computer algebra system. We demonstrate with tests and timings the effectively polynomial performance of the Butler-Portugal algorithm with respect to the number of indices, though we also show a case in which it is exponential. Our implementation handles generic tensorial expressions with several dozen indices in hundredths of a second, or one hundred indices in a few seconds, clearly outperforming all other current canonicalizers. The code has been already under intensive testing for several years and has been essential in recent investigations in large-scale tensor computer algebra.

Program summary

Program title: xPermCatalogue identifier: AEBH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBH_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.: 93 582No. of bytes in distributed program, including test data, etc.: 1 537 832Distribution format: tar.gzProgramming language: C and Mathematica (version 5.0 or higher)Computer: Any computer running C and Mathematica (version 5.0 or higher)Operating system: Linux, Unix, Windows XP, MacOSRAM:: 20 MbyteWord size: 64 or 32 bitsClassification: 1.5, 5Nature of problem: Canonicalization of indexed expressions with respect to permutation symmetries.Solution method: The Butler-Portugal algorithm.Restrictions: Multiterm symmetries are not considered.Running time: A few seconds with generic expressions of up to 100 indices. The xPermDoc.nb notebook supplied with the distribution takes approximately one and a half hours to execute in full.     

SNEG – Mathematica package for symbolic calculations with second-quantization-operator expressions

In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears advantageous to write numerical computer codes which allow the user to define the problem and the quantities of interest directly in terms of operator strings, rather than in some low-level programming language. Here I describe a Mathematica package which provides a flexible framework for performing the required translations between several different representations of operator expressions: condensed notation using pure ASCII character strings, traditional notation (“pretty printing”), internal Mathematica representation using nested lists (used for automatic symbolic manipulations), and various higher-level (“macro”) expressions. The package consists of a collection of transformation rules that define the algebra of operators and a comprehensive library of utility functions. While the emphasis is given on the problems from solid-state and atomic physics, the package can be easily adapted to any given problem involving non-commuting operators. It can be used for educational and demonstration purposes, but also for direct calculations of problems of moderate size.

Program summary

Program title: SNEGCatalogue identifier: AEJL_vl_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJL_vl_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenseNo. of lines in distributed program, including test data, etc.: 319 808No. of bytes in distributed program, including test data, etc.: 1 081 247Distribution format: tar.gzProgramming language: MathematicaComputer: Any computer which runs MathematicaOperating system: Any OS which runs MathematicaRAM: Problem dependentClassification: 2.9, 5, 6.2Nature of problem: Manipulation of expressions involving second-quantization operators and other non-commuting objects. Calculation of commutators, anticommutators, expectation values. Generation of matrix representations of the Hamiltonians expressed in the second-quantization language.Solution method: Automatic reordering of operator strings in some well specified canonical order; (anti)commutation rules are used where needed. States may be represented in occupation-number representation. Dirac bra–ket notation may be intermixed with non-commuting operator expressions.Restrictions: For very long operator strings, the brute-force automatic reordering becomes slow, but it can be turned off. In such cases, the expectation values may still be evaluated using Wick?s theorem.Unusual features: SNEG provides the natural notation of second-quantization operators (dagger for creation operators, etc.) when used interactively using the Mathematica notebook interface.Running time: Problem dependent     

QDENSITY—A Mathematica Quantum Computer simulation

This Mathematica 5.2 package¹ 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. Selected examples of the basic commands are presented here and a tutorial notebook, Tutorial.nb is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: QFT.nb, Teleportation.nb, Grover.nb and Shor.nb where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of “one way computing” ideas, are included as an additional tool in the notebook Cluster.nb. A Mathematica palette containing most commands in QDENSITY is also included: QDENSpalette.nb.

Program summary

Title of program: QDENSITYCatalogue identifier: ADXH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v1_0Program available from: CPC Program Library, Queen's University of Belfast, N. IrelandOperating systems: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4Programming language used: Mathematica 5.2No. of bytes in distributed program, including test data, etc.: 180 581No. of lines in distributed program, including test data, etc.: 19 382Distribution format: tar.gzMethod of solution: 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.     

HypExp 2, expanding hypergeometric functions about half-integer parameters

HypExp is a Mathematica package for expanding hypergeometric functions about integer and half-integer parameters.New version program summaryProgram title: HypExp 2Catalogue identifier: ADXF_v2_1Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXF_v2_1.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.: 107 274No. of bytes in distributed program, including test data, etc.: 2 690 337Distribution format: tar.gzProgramming language: Mathematica 7 and 8Computer: 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, 5Catalogue identifier of previous version: ADXF_v2_0Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 755Does 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: Compatibility with new versions of Mathematica.Summary of revisions: Support for versions 7 and 8 of Mathematica added. No changes in the features of the package.Restrictions: The classes of hypergeometric functions with half-integer parameters that can be expanded are listed in the long write-up.Additional comments: The package uses the package HPL included in the distribution.Running time: Depending on the expansion.     

Line-by-line spectroscopic simulations on graphics processing units

We report here on software that performs line-by-line spectroscopic simulations on gases. Elaborate models (such as narrow band and correlated-K) are accurate and efficient for bands where various components are not simultaneously and significantly active. Line-by-line is probably the most accurate model in the infrared for blends of gases that contain high proportions of H₂O and CO₂ as this was the case for our prototype simulation. Our implementation on graphics processing units sustains a speedup close to 330 on computation-intensive tasks and 12 on memory intensive tasks compared to implementations on one core of high-end processors. This speedup is due to data parallelism, efficient memory access for specific patterns and some dedicated hardware operators only available in graphics processing units. It is obtained leaving most of processor resources available and it would scale linearly with the number of graphics processing units in parallel machines. Line-by-line simulation coupled with simulation of fluid dynamics was long believed to be economically intractable but our work shows that it could be done with some affordable additional resources compared to what is necessary to perform simulations on fluid dynamics alone.

Program summary

Program title: GPU4RECatalogue identifier: ADZY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZY_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.: 62 776No. of bytes in distributed program, including test data, etc.: 1 513 247Distribution format: tar.gzProgramming language: C++Computer: x86 PCOperating system: Linux, Microsoft Windows. Compilation requires either gcc/g++ under Linux or Visual C++ 2003/2005 and Cygwin under Windows. It has been tested using gcc 4.1.2 under Ubuntu Linux 7.04 and using Visual C++ 2005 with Cygwin 1.5.24 under Windows XP.RAM: 1 gigabyteClassification: 21.2External routines: OpenGL (http://www.opengl.org)Nature of problem: Simulating radiative transfer on high-temperature high-pressure gases.Solution method: Line-by-line Monte-Carlo ray-tracing.Unusual features: Parallel computations are moved to the GPU.Additional comments: nVidia GeForce 7000 or ATI Radeon X1000 series graphics processing unit is required.Running time: A few minutes.     

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.     

SusyMath: A Mathematica package for quantum superfield calculations

SusyMath is a Mathematica package for quantum superfield calculations. It defines a standard form to translate the correction to the effective action corresponding to a given supergraph into a Mathematica expression, which is then evaluated and simplified. Several functions for manipulations of these expressions are provided, and the package also has the ability to save the outcomes of its calculations in form.

Program summary

Title of program: SusyMathCatalogue identifier:ADYQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYQ_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland, also at http://fma.if.usp.br/~alysson/SusyMathLicensing provisions: LGPL, CPC non-profit use licenseProgramming language: MathematicaPlatform: Any platform supporting Mathematica 4.0 or higherComputer tested on: PC (Athlon64 X2 +3800); 1 GB RAMOperating system under which the program has been tested: Linux (Debian 4.0); XOrg 7.0.22; Mathematica 5.2No. of lines in distributed program, including test data, etc.:42 472No. of bytes in distributed program, including test data, etc.:471 596Distribution format:tar.gzNature of the problem: Evaluate quantum corrections to the effective action of supersymmetric field theories, formulated in the superfield formalism, both in three- and four-spacetime dimensions.Solution method: A set of procedures for integration by parts, application of the algebra of covariant derivatives and Grassman integration, along with several auxiliary functions, is introduced.Restrictions: At the moment, the background field method is not implemented, but the system is designed to be further generalized.Running time: Depends on the complexity of the problem. From seconds for simpler one-loop diagrams to several hours for simple two-loop graphs.     

SUSY Les Houches Accord 2 I/O made easy

A library for reading and writing data in the SUSY Les Houches Accord 2 format is presented. The implementation is in native Fortran 77. The data are contained in a single array conveniently indexed by preprocessor statements.

Program summary

Program title: SLHA2LibCatalogue identifier: AEDY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDY_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.: 7550No. of bytes in distributed program, including test data, etc.: 160 123Distribution format: tar.gzProgramming language: FortranComputer: For the build process, a Fortran 77 compiler in a Unixish environment (make, shell) are requiredOperating system: Linux, Mac OS, Windows (Cygwin), Tru64 UnixRAM: The SLHA Record is currently 88 944 bytes longClassification: 4.14, 11.6Nature of problem: Exchange of SUSY parameters and decay information in an ASCII file format.Solution method: The SLHA2Lib provides routines for reading and writing files in the SUSY Les Houches Accord 2 format, a common interchange format for SUSY parameters and decay data.Restrictions: The fixed-sized array that holds the SLHA2 data necessarily limits the amount of decay data that can be stored. This limit can be enlarged by editing and re-running the SLHA2.m program.Unusual features: Data are transported in a single “double complex” array in Fortran, indexed through preprocessor macros. This is about the simplest conceivable container and needs neither dynamic memory allocation nor Fortran extension like structures.Running time: Both reading and writing a SLHA file are typically in the range of a few milliseconds.     

Gaussian quadrature rule for arbitrary weight function and interval

A program for calculating abscissas and weights of Gaussian quadrature rules for arbitrary weight functions and intervals is reported. The program is written in Mathematica. The only requirement is that the moments of the weight function can be evaluated analytically in Mathematica. The result is a FORTRAN subroutine ready to be utilized for quadrature.

Program summary

Title of program: AWGQCatalogue identifier:ADVBProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVBProgram obtained from: CPC Program Library, Queens University, Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested:Computers: Pentium IV 1.7 GHz processorInstallations: 512 MB RAMOperating systems or monitors under which the program has been tested: Windows XPProgramming language used: Mathematica 4.0No. of processors used: 1Has the code been vectorized or parallelized?: NoNo. of lines in distributed program, including test data, etc.:1076No. of bytes in distributed program, including test data, etc.: 32 681Operating systems under which program has been tested: FORTRANDistribution format: tar.gzNature of physical problem: Integration of functions.Method of solution: The recurrence relations defining the orthogonal polynomials for arbitrary weight function and integration interval are written in matrix form. The abscissas and weights for the corresponding Gaussian quadrature are found from the solution of the eigenvalue equation for the tridiagonal symmetric Jacobi matrix.Restrictions on the complexity of the problem: The program is applicable if the moments of the weight function can be evaluated analytically in Mathematica. For our test example the degree of the Gaussian quadrature cannot not be larger than 96.Typical running time: The running time of the test run is about 1 [s] with a Pentium IV 1.7 GHz processor.     

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.     

Kranc: a Mathematica package to generate numerical codes for tensorial evolution equations

We present a suite of Mathematica-based computer-algebra packages, termed “Kranc”, which comprise a toolbox to convert certain (tensorial) systems of partial differential evolution equations to parallelized C or Fortran code for solving initial boundary value problems. Kranc can be used as a “rapid prototyping” system for physicists or mathematicians handling very complicated systems of partial differential equations, but through integration into the Cactus computational toolkit we can also produce efficient parallelized production codes. Our work is motivated by the field of numerical relativity, where Kranc is used as a research tool by the authors. In this paper we describe the design and implementation of both the Mathematica packages and the resulting code, we discuss some example applications, and provide results on the performance of an example numerical code for the Einstein equations.

Program summary

Title of program: KrancCatalogue identifier: ADXS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXS_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandDistribution format: tar.gzComputer for which the program is designed and others on which it has been tested: General computers which run Mathematica (for code generation) and Cactus (for numerical simulations), tested under LinuxProgramming language used: Mathematica, C, Fortran 90Memory required to execute with typical data: This depends on the number of variables and gridsize, the included ADM example requires 4308 KBHas the code been vectorized or parallelized: The code is parallelized based on the Cactus framework.Number of bytes in distributed program, including test data, etc.: 1 578 142Number of lines in distributed program, including test data, etc.: 11 711Nature of physical problem: Solution of partial differential equations in three space dimensions, which are formulated as an initial value problem. In particular, the program is geared towards handling very complex tensorial equations as they appear, e.g., in numerical relativity. The worked out examples comprise the Klein-Gordon equations, the Maxwell equations, and the ADM formulation of the Einstein equations.Method of solution: The method of numerical solution is finite differencing and method of lines time integration, the numerical code is generated through a high level Mathematica interface.Restrictions on the complexity of the program: Typical numerical relativity applications will contain up to several dozen evolution variables and thousands of source terms, Cactus applications have shown scaling up to several thousand processors and grid sizes exceeding 500³.Typical running time: This depends on the number of variables and the grid size: the included ADM example takes approximately 100 seconds on a 1600 MHz Intel Pentium M processor.Unusual features of the program: based on Mathematica and Cactus     

LevelScheme: A level scheme drawing and scientific figure preparation system for Mathematica

LevelScheme is a scientific figure preparation system for Mathematica. The main emphasis is upon the construction of level schemes, or level energy diagrams, as used in nuclear, atomic, molecular, and hadronic physics. LevelScheme also provides a general infrastructure for the preparation of publication-quality figures, including support for multipanel and inset plotting, customizable tick mark generation, and various drawing and labeling tasks. Coupled with Mathematica's plotting functions and powerful programming language, LevelScheme provides a flexible system for the creation of figures combining diagrams, mathematical plots, and data plots.

Program summary

Title of program:LevelSchemeCatalogue identifier:ADVZProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVZOperating systems:Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and LinuxProgramming language used:Mathematica 4Number of bytes in distributed program, including test and documentation:3 051 807Distribution format:tar.gzNature of problem:Creation of level scheme diagrams. Creation of publication-quality multipart figures incorporating diagrams and plots.Method of solution:A set of Mathematica packages has been developed, providing a library of level scheme drawing objects, tools for figure construction and labeling, and control code for producing the graphics.