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     

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.     

FeynEdit—a tool for drawing Feynman diagrams

We describe the FeynEdit tool for drawing Feynman diagrams. Input and output is done using the macros of FeynArts, which also implies that diagrams drawn by FeynArts can be edited with FeynEdit. The code can be conveniently transferred using copy-and-paste.

Program summary

Program title: FeynEditCatalogue identifier: AEBX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBX_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.: 31 729No. of bytes in distributed program, including test data, etc.: 500 240Distribution format: tar.gzProgramming language: JavaComputer: All Java-capable platformsOperating system: Linux, Mac OS, WindowsRAM: 1-2 MBytesClassification: 4.4Nature of problem: Graphical editing of Feynman diagrams.Solution method: The user copy-and-pastes the LaTeX code of the Feynman diagram into the editor, clicks a button to visualize the diagram, modifies it using the mouse, and finally copy-and-pastes it back into the text.Restrictions: Propagators are presently drawn only as straight lines. This is largely for performance reasons and may be added in a future version. It is not a serious deficit because that information can easily be added in the LaTeX code.Unusual features: Uses FeynArts' LaTeX representation for input and outputRunning time: User-dependent     

FeynRules - Feynman rules made easy

In this paper we present FeynRules, a new Mathematica package that facilitates the implementation of new particle physics models. After the user implements the basic model information (e.g., particle content, parameters and Lagrangian), FeynRules derives the Feynman rules and stores them in a generic form suitable for translation to any Feynman diagram calculation program. The model can then be translated to the format specific to a particular Feynman diagram calculator via FeynRules translation interfaces. Such interfaces have been written for CalcHEP/CompHEP, FeynArts/FormCalc, MadGraph/MadEvent and Sherpa, making it possible to write a new model once and have it work in all of these programs. In this paper, we describe how to implement a new model, generate the Feynman rules, use a generic translation interface, and write a new translation interface. We also discuss the details of the FeynRules code.

Program summary

Program title: FeynRulesCatalogue identifier: AEDI_v1_0Program summary URL::http://cpc.cs.qub.ac.uk/summaries/AEDI_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.: 15 980No. of bytes in distributed program, including test data, etc.: 137 383Distribution format: tar.gzProgramming language: MathematicaComputer: Platforms on which Mathematica is availableOperating system: Operating systems on which Mathematica is availableClassification: 11.1, 11.2, 11.6Nature of problem: Automatic derivation of Feynman rules from a Lagrangian. Implementation of new models into Monte Carlo event generators and FeynArts.Solution method: FeynRules works in two steps:

1. derivation of the Feynman rules directly form the Lagrangian using canonical commutation relations among fields and creation operators.

2. implementation of the new physics model into FeynArts as well as various Monte Carlo programs via interfaces.

Full-size table

     

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.     

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.     

HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters

We present the Mathematica package HypExp which allows to expand hypergeometric functions around integer parameters to arbitrary order. At this, we apply two methods, the first one being based on an integral representation, the second one on the nested sums approach. The expansion works for both symbolic argument z and unit argument. We also implemented new classes of integrals that appear in the first method and that are, in part, yet unknown to Mathematica.

Program summary

Title of program:HypExpCatalogue identifier:ADXF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXF_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicence:noneComputers:Computers running Mathematica under Linux or WindowsOperating system:Linux, WindowsProgram language:MathematicaNo. of bytes in distributed program, including test data, etc.:739 410No. of lines in distributed program, including test data, etc.:89 747Distribution format:tar.gzOther package needed:the package HPL, included in the distributionExternal file required:noneNature of the physical problem:Expansion of hypergeometric functions around integer-valued parameters. These are needed in the context of dimensional regularization for loop and phase space integrals.Method of solution:Algebraic manipulation of nested sums and integral representation.Restrictions on complexity of the problem:Limited by the memory availableTypical running time:Strongly depending on the problem and the availability of libraries.     

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.     

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.     

The MATHSCOUT Mathematica package to postprocess the output of other scientific programs

mathscout is a mathematica¹ package to postprocess the output of other programs for scientific calculations. We wrote mathscout to import data from a major program for ab initio computational chemistry into mathematica, so that we could postprocess the chemical results. It can be used to import the output of many other packages that are used, e.g. in molecular dynamics, crystallography, spectroscopic analysis, metabolic and physiological modeling, meteorology and other areas of environmental science, cosmology and particle physics. mathscout assigns a name to each table and non-tabular datum that it extracts. This name is constructed mechanically from the identifier or phrase that precedes or follows or embeds the item in the output that mathscout processes. A selection of non-contiguous items, or all the items in a section of the file, or in the entire file are extracted using simple commands. So far, we have focused on our immediate needs to postprocess the output of the Gaussian² program. Calculations on several molecules that illustrate the usage of the package are presented here and in the Supplementary Information. mathscout is shortened to msct in the software.

Program summary

Program title: msct.mCatalogue identifier: ADZQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZQ_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.: 30 396No. of bytes in distributed program, including test data, etc.: 1 799 469Distribution format: tar.gzProgramming language: MathematicaComputer: Any computer running unix and MathematicaOperating system: UnixSupplementary material: The Development guideClassification: 4.14, 5, 16.1, 20Nature of problem: Import data from output files of scientific computing packages, such as Gaussian, into Mathematica for symbolic calculation and production of publication quality tables and plots.Solution method: Provision of mnemonic top-down parsing procedures, functional programming.Running time: The complete extraction of data from a small basis density functional calculation on the water molecule, and from a larger basis density functional calculation on the zinc hydrate ion, that ran to 33 iterations, took 1 second and 23 seconds, respectively, on a Dell Poweredge 1750.     

A superspace module for the FeynRules package

We describe an additional module for the Mathematica package FeynRules that allows for an easy building of any N=1 supersymmetric quantum field theory, directly in superspace. After the superfield content of a specific model has been implemented, the user can study the properties of the model, such as the supersymmetric transformation laws of the associated Lagrangian, directly in Mathematica. While the model dependent parts of the latter, i.e., the soft supersymmetry-breaking Lagrangian and the superpotential, have to be provided by the user, the model independent pieces, such as the gauge interaction terms, are derived automatically. Using the strengths of the FeynRules program, it is then possible to derive all the Feynman rules associated to the model and implement them in all the Feynman diagram calculators interfaced to FeynRules in a straightforward way.

Program summary

Program title: “FeynRules”Catalogue identifier: AEDI_v1_1Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDI_v1_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.: 46 491No. of bytes in distributed program, including test data, etc.: 381 582Distribution format: tar.gzProgramming language: MathematicaComputer: Platforms on which Mathematica is availableOperating system: Operating systems on which Mathematica is availableClassification: 11.1, 11.6Catalogue identifier of previous version: AEDI_v1_0Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 1614Does the new version supersede the previous version?: NoNature of problem: Study of the properties of N=1 supersymmetric field theories using the superfield formalism, derivation of the associated Lagrangians.Solution method: We use the FeynRules package and define internally the N=1 superspace. Then, we implement a module allowing to:

• 1. 

  Perform the Grassmann variable series expansion so that any superfield expression can be developed in terms of the component fields. The resulting expression is thus suitable to be treated by the FeynRules package directly.

• 2. 

  Execute a set of operations associated to the superspace, such as the superderivatives of an expression or the calculation of its supersymmetric transformation laws.

Reasons for new version: This is an interim update to the FeynRules-1.4 (AEDI_v1_0), package which includes a new superspace module. Further modules will be added in the future and eventually published as FeynRules-1.6.Summary of revisions: This revised version contains, in addition to the core program, the superfield module of FeynRules.Restrictions: Superfields related to spin 3/2 and 2 particles are not implemented.Unusual features: All calculations in the internal routines are performed completely. The only hardcoded core is the Grassmann variable algebra.Running time: It depends on the user?s purposes. The extraction of a Lagrangian in terms of the component fields may take a few minutes for a complete model with complex mixing between the fields.     

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.     

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.     

STRINGVACUA. A Mathematica package for studying vacuum configurations in string phenomenology

We give a simple tutorial introduction to the Mathematica package STRINGVACUA, which is designed to find vacua of string-derived or inspired four-dimensional N=1 supergravities. The package uses powerful algebro-geometric methods, as implemented in the free computer algebra system Singular, but requires no knowledge of the mathematics upon which it is based. A series of easy-to-use Mathematica modules are provided which can be used both in string theory and in more general applications requiring fast polynomial computations. The use of these modules is illustrated throughout with simple examples.

Program summary

Program title: STRINGVACUACatalogue identifier: AEBZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBZ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU GPLNo. of lines in distributed program, including test data, etc.: 31 050No. of bytes in distributed program, including test data, etc.: 163 832Distribution format: tar.gzProgramming language: “Mathematica” syntaxComputer: Home and office spec desktop and laptop machines, networked or stand aloneOperating system: Windows XP (with Cygwin), Linux, Mac OS, running Mathematica V5 or aboveRAM: Varies greatly depending on calculation to be performedClassification: 11.1External routines: Linux: The program “Singular” is called from Mathematica. Windows: “Singular” is called within the Cygwin environment from Mathematica.Nature of problem: A central problem of string-phenomenology is to find stable vacua in the four-dimensional effective theories which result from compactification.Solution method: We present an algorithmic method, which uses techniques of algebraic geometry, to find all of the vacua of any given string-phenomenological system in a huge class.Running time: Varies greatly depending on calculation requested.     

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.     

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.     

Beam-plasma dielectric tensor with Mathematica

We present a Mathematica notebook allowing for the symbolic calculation of the 3×3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma.

Program summary

Title of program: TensorCatalog identifier: ADYT_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, SpainOperating system under which the program has been tested: Windows XP ProProgramming language used: Mathematica 4.1Memory required to execute with typical data: 7.17 MbytesNo. of bytes in distributed program, including test data, etc.: 33 439No. of lines in distributed program, including test data, etc.: 3169Distribution format: tar.gzNature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables.Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère-Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the dimensionless variables.Restrictions on the complexity of the problem: Temperature effects are limited to small, i.e. non-relativistic, temperatures. The kinetic counterpart of the present Mathematica will usually not compute the required integrals.Typical running time: About 1 minute on a Intel Centrino 1.5 GHz Laptop with 512 MB of RAM.Unusual features of the program: None.     

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.