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.     

-XSummer- Transcendental functions and symbolic summation in Form

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example, from the expansion of generalized hypergeometric functions around integer values of the parameters. In this paper we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.

Program summary

Title of program:XSummerCatalogue identifier:ADXQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXQ_v1_0Program obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandLicense:GNU Public License and Form LicenseComputers:allOperating system:allProgram language:FormMemory required to execute:Depending on the complexity of the problem, recommended at least 64 MB RAMNo. of lines in distributed program, including test data, etc.:9854No. of bytes in distributed program, including test data, etc.:126 551Distribution format:tar.gzOther programs called:noneExternal files needed:noneNature of the physical problem:Systematic expansion of higher transcendental functions in a small parameter. The expansions arise in the calculation of loop integrals in perturbative quantum field theory.Method of solution:Algebraic manipulations of nested sums.Restrictions on complexity of the problem:Usually limited only by the available disk space.Typical running time:Dependent on the complexity of the problem.     

Automatized analytic continuation of Mellin-Barnes integrals

This paper describe a package written in MATHEMATICA that automatizes typical operations performed during evaluation of Feynman graphs with Mellin-Barnes (MB) techniques. The main procedure allows to analytically continue a MB integral in a given parameter without any intervention from the user and thus to resolve the singularity structure in this parameter. The package can also perform numerical integrations at specified kinematic points, as long as the integrands have satisfactory convergence properties. It is demonstrated that, at least in the case of massive graphs in the physical region, the convergence may turn out to be poor, making naïve numerical integration of MB integrals unusable. Possible solutions to this problem are presented, but full automatization in such cases may not be achievable.

Program summary

Title of program: MBProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYG_v1_0Catalogue identifier: ADYG_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputers: AllOperating systems: AllProgramming language used:MATHEMATICA, Fortran 77 for numerical evaluationMemory required to execute with typical data: Sufficient for a typical installation of MATHEMATICA.No. of lines in distributed program, including test data, etc.: 12 013No. of bytes in distributed program, including test data, etc.: 231 899Distribution format: tar.gzLibraries used:CUBA [T. Hahn, Comput. Phys. Commun. 168 (2005) 78] for numerical evaluation of multidimensional integrals and CERNlib [CERN Program Library, obtainable from: http://cernlib.web.cern.ch/cernlib/] for the implementation of Γ and ψ functions in Fortran.Nature of physical problem: Analytic continuation of Mellin-Barnes integrals in a parameter and subsequent numerical evaluation. This is necessary for evaluation of Feynman integrals from Mellin-Barnes representations.Method of solution: Recursive accumulation of residue terms occurring when singularities cross integration contours. Numerical integration of multidimensional integrals with the help of the CUBA library.Restrictions on the complexity of the problem: Limited by the size of the available storage space.Typical running time: Depending on the problem. Usually seconds for moderate dimensionality integrals.     

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.     

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     

AMBRE—a Mathematica package for the construction of Mellin-Barnes representations for Feynman integrals

The Mathematica toolkit AMBRE derives Mellin-Barnes (MB) representations for Feynman integrals in d=4−2ε dimensions. It may be applied for tadpoles as well as for multi-leg multi-loop scalar and tensor integrals. The package uses a loop-by-loop approach and aims at lowest dimensions of the final MB representations. The present version works fine for planar Feynman diagrams. The output may be further processed by the package MB for the determination of its singularity structure in ε. The AMBRE package contains various sample applications for Feynman integrals with up to six external particles and up to four loops.

Program summary

Program title:AMBRECatalogue identifier:ADZR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZR_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.:21 387No. of bytes in distributed program, including test data, etc.:100 004Distribution format:tar.gzProgramming language:MATHEMATICA v.5.0 and later versionsComputer:allOperating system:allRAM:sufficient for a typical installation of MATHEMATICAClassification:5; 11.1External routines:The examples in the package use:

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MB.m [M. Czakon, Comput. Phys. Commun. 175 (2006) 559 (CPC Cat. Id. ADYG)], for expansions in ε;

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CUBA [T. Hahn, Comput. Phys. Commun. 168 (2005) 78 (CPC Cat. Id. ADVH)], for numerical evaluation of multidimensional integrals;

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CERNlib [CERN Program Library, http://cernlib.web.cern.ch/cernlib/], for the implementation of Γ and Ψ functions in Fortran.

Nature of problem:Derivation of a representation for a Feynman diagram with L loops and N internal lines in d dimensions by Mellin-Barnes integrals; the subsequent evaluation, after an analytical continuation in ε=(4−d)/2, has to be done with other packages.Solution method:Introduction of N Feynman parameters xi, integration over the loop momenta, and subsequent integration over x, introducing thereby representations of sums of monomials in x by Mellin-Barnes integrals.Restrictions:Limited by the size of the available storage space.Running time:Depending on the problem; usually seconds.     

Slavnov-Taylor1.0: A Mathematica package for computation in BRST formalism

Slavnov-Taylor is a Mathematica package which allows us to perform automatic symbolic computation in BRST formalism. This article serves as a self-contained guide to prospective users, and indicates the conventions and approximations used.

Program summary

Title of program:Slavnov-TaylorCatalogue identifier:ADSSProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSSProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming Language: Mathematica 4.0Platform: Any platform supporting Mathematica 4.0Computers tested on: Pentium PCOperating systems under which the program has been tested: LinuxMemory required to execute: Minimal: 1.254.784 bytes, Standard: 1.281.248 bytesNo. of bytes in distributed program, including test data, etc.: 8368 bytesDistribution format: tar gzip fileKeywords: Slavnov-Taylor, BRST, MathematicaNature of physical problem: Symbolic computation in the Slavnov-Taylor formalism for gauge theories in 4-dimensional space-time based on a semi-simple compact Lie group for a general BRS transformations.Restrictions on the complexity of the problem: Only matter in the adjoint is allowed.Typical running time: less than one second     

Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d=2 and d=4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10¹⁵ is achieved for arbitrary real values of the momentum transfer.

Program summary

Title of program:sunemVersion: 1.0Release: 1Catalogue identifier: ADYC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYC_v1_0Program obtainable from:http://www-ttp.physik.uni-karlsruhe.de/Progdata/Computers: allOperating system: allProgram language used:FORTRAN77No. of lines in distributed program, including test data, etc.:1080No. of bytes in distributed program, including test data, etc.: 11 835Memory required to execute: Size: 1532KNo. of bits in a word: up to 32No. of processors used: 1Distribution format: tar.gzOther programs called: noneExternal files needed: noneNature of the physical problem: Numerical evaluation of the two Master Integrals of the equal mass two-loop sunrise Feynman graph for arbitrary momentum transfer in d=2 and d=4 dimensions.Method of solution: Accelerated power series expansions obtained by solving the differential equations for the MIs at their singular points. With a maximum of 22 terms for the worse case expansion a relative precision of better than a part in 10¹⁵ is achieved for arbitrary real values of the momentum transfer.Restrictions on complexity of the problem: Limited to real momentum transfer and equal internal masses.Typical running time: Approximately 1 μs to evaluate the four Master integrals for a fixed momentum transfer value on a Pentium IV/3 GHz Linux PC.     

Reduze - Feynman integral reduction in C++

Reduze is a computer program for reducing Feynman integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the system of equations. Reduze offers the possibility to run reductions in parallel.

Program summary

Program title:ReduzeCatalogue identifier: AEGE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions:: yesNo. of lines in distributed program, including test data, etc.: 55 433No. of bytes in distributed program, including test data, etc.: 554 866Distribution format: tar.gzProgramming language: C++Computer: AllOperating system: Unix/LinuxNumber of processors used: The number of processors is problem dependent. More than one possible but not arbitrary many.RAM: Depends on the complexity of the system.Classification: 4.4, 5External routines: CLN (http://www.ginac.de/CLN/), GiNaC (http://www.ginac.de/)Nature of problem: Solving large systems of linear equations with Feynman integrals as unknowns and rational polynomials as prefactors.Solution method: Using a Gauss/Laporta algorithm to solve the system of equations.Restrictions: Limitations depend on the complexity of the system (number of equations, number of kinematic invariants).Running time: Depends on the complexity of the system.     

SaX: An open source package for electronic-structure and optical-properties calculations in the GW approximation

We present here SaX (Self-energies and eXcitations), a plane-waves package aimed at electronic-structure and optical-properties calculations in the GW framework, namely using the GW approximation for quasi-particle properties and the Bethe-Salpeter equation for the excitonic effects. The code is mostly written in FORTRAN90 in a modern style, with extensive use of data abstraction (i.e. objects). SaX employs state of the art techniques and can treat large systems. The package is released with an open source license and can be also download from http://www.sax-project.org/.

Program summary

Program title: SaX (Self-energies and eXcitations)Catalogue identifier: AEDF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDF_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.: 779 771No. of bytes in distributed program, including test data, etc.: 4 894 755Distribution format: tar.gzProgramming language: FORTRAN, plus some C utilitiesComputer: Linux PC, Linux clusters, IBM-SP5Operating system: Linux, AixHas the code been vectorised or parallelized?: YesRAM: depending on the system complexityClassification: 7.3External routines: Message-Passing Interface (MPI) to perform parallel computations. ESPRESSO (http://www.quantum-espresso.org)Nature of problem: SaX is designed to calculate the electronic band-structure of semiconductors, including quasi-particle effects and optical properties including excitonic effects.Solution method: The electronic band-structure is calculated using the GW approximation for the self-energy operator. The optical properties are calculated solving the Bethe-Salpeter equation in the GW approximation. The wavefunctions are expanded on a plane-waves basis set, using norm-conserving pseudopotentials.Restrictions: Many objects are non-local matrix represented in plane wave basis sets. The memory required by the program in the allocation of such objects increases with the increase of the simulation cell volume. Other quantities are built calculating electronic transitions, so that the computational time increase with their number, and scales as , where Nv and Nc are the number of valence and conduction bands implied in the transition and Nk is the number of special k vectors. Symmetries are not exploited yet. Finally, metallic systems cannot be studied yet.Unusual features: SaX is written using FORTRAN90 in an object-oriented way. Thus, it is easy to add new features and to reuse the code.Running time: The 3 examples, contained in the distribution file, each take only a few seconds to run. For systems of interest, the run may take a number of days with a typical memory allocation of 1600 Mb per processor.     

Class library ranlip for multivariate nonuniform random variate generation

This paper describes generation of nonuniform random variates from Lipschitz-continuous densities using acceptance/rejection, and the class library ranlip which implements this method. It is assumed that the required distribution has Lipschitz-continuous density, which is either given analytically or as a black box. The algorithm builds a piecewise constant upper approximation to the density (the hat function), using a large number of its values and subdivision of the domain into hyperrectangles.The class library ranlip provides very competitive preprocessing and generation times, and yields small rejection constant, which is a measure of efficiency of the generation step. It exhibits good performance for up to five variables, and provides the user with a black box nonuniform random variate generator for a large class of distributions, in particular, multimodal distributions. It will be valuable for researchers who frequently face the task of sampling from unusual distributions, for which specialized random variate generators are not available.

Program summary

Title of program: RanlipCatalogue number: ADVPProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVPProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputers: IBM PC; DEC AlphaOperating systems under which the program has been tested: Windows XP, Linux, UnixProgramming language used: C++Memory required to execute with typical data: 32MNo. of bits in a word: 32No. of processors used: 1Has the code been vectorized?: NoNo. of lines in distributed program, including test data, etc.: 52 160No. of bytes in distributed program, including test data, etc.: 392 625Distribution format: tar.gzNature of physical problem:This program allows one to generate nonuniform random vectors from a variety of distributions (especially multimodal), using acceptance/rejection approach. Suitable for non-standard distributions for up to five variables.Method of solution:Assuming Lipschitz-continuous density, a tight overestimate (the hat function) is computed. Then random variates are generated using acceptance/rejection approach.Restrictions on the complexity of the problem:If the number of variables exceeds five, computation of the overestimate is inefficient.Typical running time:Preprocessing 1-5000 s, generation .     

spinney: A Form library for helicity spinors

In this work, the library spinney is presented, which provides an implementation of helicity spinors and related algorithms for the symbolical manipulation program Form. The package is well suited for symbolic amplitude calculations both in traditional, Feynman diagram based approaches and unitarity-based techniques.

Program summary

Program title: spinneyCatalogue identifier: AEJQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJQ_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.: 21 128No. of bytes in distributed program, including test data, etc.: 377 589Distribution format: tar.gzProgramming language: FormComputer: Any supporting the Form languageOperating system: Any supporting the Form languageClassification: 4.4, 5, 11.1Nature of problem: Implementation of the spinor-helicity formalismSolution method: Form implementationRunning time: From actual calculations of all six-point one-loop diagrams of the process bounds of 50 ms<t?71 s for the simplest and the most complicated diagram respectively have been derived on an Intel Xeon 3.20 GHz using Form 3.3.     

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.     

SuperIso Relic: A program for calculating relic density and flavor physics observables in Supersymmetry

We describe SuperIso Relic, a public program for evaluation of relic density and flavor physics observables in the minimal supersymmetric extension of the Standard Model (MSSM). SuperIso Relic is an extension of the SuperIso program which adds to the flavor observables of SuperIso the computation of all possible annihilation and coannihilation processes of the LSP which are required for the relic density calculation. All amplitudes have been generated at the tree level with FeynArts/FormCalc, and widths of the Higgs bosons are computed with FeynHiggs at the two-loop level. SuperIso Relic also provides the possibility to modify the assumptions of the cosmological model, and to study their consequences on the relic density.

Program summary

Program title: SuperIso RelicCatalogue identifier: AEGD_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGD_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: yesNo. of lines in distributed program, including test data, etc.: 2 274 720No. of bytes in distributed program, including test data, etc.: 6 735 649Distribution format: tar.gzProgramming language: C (C99 Standard compliant) and FortranComputer: 32- or 64-bit PC, MacOperating system: Linux, MacOSRAM: 100 MbClassification: 1.9, 11.6External routines: ISASUGRA/ISAJET and/or SOFTSUSY, FeynHiggsDoes the new version supersede the previous version?: No (AEAN_v2_0)Nature of problem: Calculation of the lightest supersymmetric particle relic density, as well as flavor physics observables, in order to derive constraints on the supersymmetric parameter space.Solution method: SuperIso Relic uses a SUSY Les Houches Accord file, which can be either generated automatically via a call to SOFTSUSY or ISAJET, or provided by the user. This file contains the masses and couplings of the supersymmetric particles. SuperIso Relic then computes the lightest supersymmetric particle relic density as well as the most constraining flavor physics observables. To do so, it calculates first the widths of the Higgs bosons with FeynHiggs, and then it evaluates the squared amplitudes of the diagrams needed for the relic density calculation. These thousands of diagrams have been previously generated with the FeynArts/FormCalc package. SuperIso Relic is able to perform the calculations in different supersymmetry breaking scenarios, such as mSUGRA, NUHM, AMSB and GMSB.Reasons for new version: This version incorporates the calculation of the relic density, which is often used to constrain Supersymmetry.Summary of revisions:

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Addition of the relic density calculation

•

Replacement of "float" type by "double".

Unusual features: SuperIso Relic includes the possibility of altering the underlying cosmological model and testing the influence of the cosmological assumptions.Additional comments: This program is closely associated with the "SuperIso" program - CPC Program Library, Catalogue Id. AEAN.Running time:Compilation time: a couple of hours for the statically linked version, a few minutes for the dynamically linked version. Running time: about 1 second, or a few seconds if libraries need to be compiled on the fly.     

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.     

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.     

Optimising code generation with haggies

This article describes haggies, a program for the generation of optimised programs for the efficient numerical evaluation of mathematical expressions. It uses a multivariate Horner-scheme and Common Subexpression Elimination to reduce the overall number of operations.The package can serve as a back-end for virtually any general purpose computer algebra program. Built-in type inference that allows to deal with non-standard data types in strongly typed languages and a very flexible, pattern-based output specification ensure that haggies can produce code for a large variety of programming languages.We currently use haggies as part of an automated package for the calculation of one-loop scattering amplitudes in quantum field theories. The examples in this articles, however, demonstrate that its use is not restricted to the field of high energy physics.

Program summary

Program title: haggiesCatalogue identifier: AEGF_v1_0Program summary: URL: http://cpc.cs.qub.ac.uk/summaries/AEGF_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 56 220No. of bytes in distributed program, including test data, etc.: 579 010Distribution format: tar.gzProgramming language: Java, JavaCCComputer: Any system that runs the Java Virtual MachineOperating system: Any system that runs the Java Virtual MachineRAM: Determined by the size of the problemClassification: 4.14, 5, 6.2, 6.5, 11.1Nature of problem: Generation of optimised programs for the evaluation of possibly large algebraic expressionsSolution method: Java implementationRunning time: Determined by the size of the problem     

TSIL: a program for the calculation of two-loop self-energy integrals

TSIL is a library of utilities for the numerical calculation of dimensionally regularized two-loop self-energy integrals. A convenient basis for these functions is given by the integrals obtained at the end of O.V. Tarasov's recurrence relation algorithm. The program computes the values of all of these basis functions, for arbitrary input masses and external momentum. When analytical expressions in terms of polylogarithms are available, they are used. Otherwise, the evaluation proceeds by a Runge-Kutta integration of the coupled first-order differential equations for the basis integrals, using the external momentum invariant as the independent variable. The starting point of the integration is provided by known analytic expressions at (or near) zero external momentum. The code is written in C, and may be linked from C/C++ or Fortran. A Fortran interface is provided. We describe the structure and usage of the program, and provide a simple example application. We also compute two new cases analytically, and compare all of our notations and conventions for the two-loop self-energy integrals to those used by several other groups.

Program summary

Title of program:TSILVersion number: 1.0Catalogue identifier: ADWSProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWSProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming language: CPlatform: Any platform supporting the GNU Compiler Collection (gcc), the Intel C compiler (icc), or a similar C compiler with support for complex mathematicsNo. of lines in distributed program, including test data, etc.: 42 730No. of bytes in distributed program, including test data, etc.: 297 101Distribution format: tar.gzNature of physical problem: Numerical evaluation of dimensionally regulated Feynman integrals needed in two-loop self-energy calculations in relativistic quantum field theory in four dimensions.Method of solution: Analytical evaluation in terms of polylogarithms when possible, otherwise through Runge-Kutta solution of differential equations.Limitations: Loss of accuracy in some unnatural threshold cases that do not have vanishing masses.Typical running time: Less than a second.     

Package for calculations and simplifications of expressions with Dirac matrices (MatrixExp)

This paper describes a package for calculations of expressions with Dirac matrices. Advantages over existing similar packages are described. MatrixExp package is intended for simplification of complex expressions involving γ-matrices, providing such tools as automatic Feynman parameterization, integration in d-dimensional space, sorting and grouping of results in a given order. Also, in comparison with the existing similar package Tracer, the presented package MatrixExp has more enhanced input possibility. User-available functions of MatrixExp package are described in detail. Also an example of calculation of Feynman diagram for process b→sγg with application of functions of MatrixExp package is presented.

Program summary

Title of program:MatrixExpCatalogue identifier:ADWBProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWBProgram obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:noneProgramming language:MATHEMATICAComputer:PC PentiumOperating system:WindowsNo. of lines in distributed program, including test data, etc.: 1551No. of bytes in distributed program, including test data, etc.: 16 040Distribution format:tar.gzRAM:loading the package uses approx. 3 500 000 bytes of RAM. However memory required for calculations depends heavily on the expressions in the view, as the package uses recursive functions, and MATHEMATICA dynamically allocates memory. Package has been tested to work on PC Pentium II 233 MHz with 128 Mb of memory calculating typical diagrams of contemporary calculations.Nature of problem:Feynman diagram calculation, simplification of expressions with γ-matricesSolution method:Analytic transformations, dimensional regularization, Feynman parameterizationRestrictions:MatrixExp package works only with single line of expressions (G[l1,]), in contrast to the Tracer package that works with multiple lines, i.e., the following is possible in Tracer, but not in MatrixExp: G[l1,]**G[l2,]**G[l3,], which will return the result of G[l1,]**G[l1,]**G[l1,]….Unusual features:noneRunning time:Seconds for expressions with several different γ-matrices on Pentium IV 1.8 GHz and of the order of a minute on Pentium II 233 MHz. Calculation times rise with the number of matrices.