Review of the Robotica software package for robotic manipulators

Robotica is a computer-aided design package for robotic nmanipulators developed at the Coordinated Science Laboratory at the University of Illinois at Urbana- Champaign. The package is a collection of function definitions for the Mathematica symbolic mathematics program. Robotica can be used either with an X- Windows graphical user interface (GUI) on a Sun Workstation or as an included function definition file within Mathematica. The primary feature of Robotica is the ability to compute, symbolically or numerically, the kinematic and dynamic equations of arbitrary robot systems utilizing the standard Denevit-Hartenburg (DH) kinematic convention. Robotica also provides the ability to visualize these arbitrary manipulators using the X- Windows graphical interface to the Mathematica graphics routines. The paper looks at the usage of Robotica at the Air Force Institute of Technology, comments on the features of Robotica, and needs for improvement and suggestions for future development     

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.     

Simulation of n-R planar manipulators

Modeling and simulation of n-DOF planar manipulators with revolute joints are presented in the paper. First, numerical effective equations to solve the direct kinematics of n-degree-of-freedom manipulators are derived. Following this, the dynamic model based on Lagrangian equation is developed. In the model the characteristics of planar manipulators are utilized and therefore the complexity of the model is increasing slower with the number of degrees of freedom compared with the general type of manipulators. Next, some cost functions for n-R manipulators and their gradients are presented. The derived models represent the basis of the software package “Planar Manipulators Toolbox” implemented in MATLAB/SIMULINK. The package allows the user to create and simulate different systems considering planar manipulators. MATLAB functions and SIMULINK blocks provided, include forward kinematics, dynamics and several utility functions.     

非线性系统观测器的计算机代数分析与设计方法*

本文介绍了控制系统非线性观测器的分析和设计方法，根据扩展Ｌｕｅｎｂｅｒｇｅｒ观测器设计过程中放大系数向量的计算公式，用计算机代数方法进行非线性观测器设计，本文给出了用Ｍａｔｈｅｍａｔｉｃａ符号编程语言实现的算法软件包，并使用该软件包对一个具体实例进行了分析和设计。     

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.     

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.     

KLEIN: a MATHEMATICA Package for Radar Polarimetry Based on Spinor and Tensor Algebra

This paper introduces and describes Klein, a Mathematica package, designed to be used as a support and verification tool for scientific calculations in radar polarimetry based on spinor and tensor algebra.     

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.     

Simulation and computer-aided kinematic design of three-degree-of-freedom spherical parallel manipulators

Parallel robotic manipulators are complex mechanical systems that lead to involved kinematic and dynamic equations. Hence, the design of such systems is in general not intuitive, and advanced simulation and design tools specialized for this type of architecture are highly desirable. This article discusses the kinematic simulation and computer-aided design of three-degree-of-freedom spherical parallel manipulators with either prismatic or revolute actuators. The kinematic analysis of spherical parallel manipulators is first reviewed. Solutions for the direct and inverse kinematic problems are given, and the expressions for the singularity loci are then introduced. The determination of the workspace of this type of manipulator is also addressed. Finally, a computer package developed specifically for the CAD of spherical parallel manipulators is presented. This package allows the interactive analysis of manipulators of arbitrary architecture including the representation of the workspace, the representation of singularities, and the graphic animation of trajectories specified either by the direct or the inverse kinematic module. It can be used for the design of any spherical parallel three-degree-of-freedom actuated mechanism, which can find many applications in high-performance robotic systems. © 3995 John Wiley & Sons, Inc.     

CRunDec: A C++ package for running and decoupling of the strong coupling and quark masses

In this paper we present the C++ package CRunDec which implements all relevant formulae needed for the running and decoupling for the strong coupling constant and light quark masses. Furthermore, several formulae are implemented which can be used to transform the heavy quark masses among different renormalization schemes. CRunDec is the C++ version on the Mathematica package RunDec containing several updates and improvements.     

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.     

Student-oriented program for introductory robotics education

The aim of the paper is to present a software package for teaching introductory robotics. One of two simple manipulators (Cartesian or cylindrical coordinates) can be chosen and joined control algorithms (PID or adaptive one) together with pointed models of acutators and sensors. Computer simulation is available in an easy way for the model parameters determined. The simulation results can be displayed as graph functions, tables or as the animal of manipulators considered.     

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.     

Mathematica as an Environment for Doing Economics and Econometrics

Today's graduate students in economics must master early on a computational environment suitable for their research needs. A case is made here why Mathematica is an eminently reasonable choice for this purpose for many students. Salient features of Mathematica are examined in this context, and the breadth of economic research accomplished in Mathematica is illustrated.     

Symbolic integration of a product of two spherical Bessel functions with an additional exponential and polynomial factor

We present a Mathematica package that performs the symbolic calculation of integrals of the form

(1)     

Computation of the Interval of Stability of Runge–Kutta–Nyström Methods

We present a Mathematica package to compute the interval of stability of Runge–Kutta–Nystrom methods fory">=f(t,y).     

xTras: A field-theory inspired xAct package for mathematica

We present the tensor computer algebra package xTras, which provides functions and methods frequently needed when doing (classical) field theory. Amongst others, it can compute contractions, make Ansätze, and solve tensorial equations. It is built upon the tensor computer algebra system xAct, a collection of packages for Mathematica.