同伦算法在特征造型中的应用

目前有很多方法用来进行几何约束的求解,每种方法都有各自的优缺点。文中在同伦法与数值法、符号代数法、分解法进行对比的同时,将其与计算机辅助设计结合起来,应用到CAD领域的特征造型中,并在自主开发的计算机辅助工业造型系统中(HUSTCAIDS)实现。     

代数符号计算的神经网络模型

文中给出一种p-adic数制式非对称连接神经网络模型,该网络在整个矢量空间只有唯一平衡点,因而可获得问题的最优解,且在存在计算误差,这种神经网络保持高度并行结构,可用了代数符号计算,本文重点分析了实现神经网络的方法,给代数符号计算提供了一个新的计算模型。     

New algorithms for the Perspective-Three-Point Problem

In this paper,two approaches are used to solve the Perspective-Three-Point Problem(P3)):the symbolic computation approach and the geometric approach.In the symbolic computation approach,we use Wu-Ritt‘s zero decomposition algorithm to give a complete triangular decomposition for the P3P equation system.This decomposition provides the firest complete analytical solution to the P3P problem.In the geometric approach,we give some pure geometric criteria for the number of real physical solutions.The complete solution classification for two special cases with three and four paramters is also given.     

Integration strategy for distributed intelligent systems

In this article, we describe a new framework for designing real-time intelligent control systems. An integrated intelligent system is a large knowledge integration environment that consists of both symbolic reasoning systems (expert systems) and numerical computation packages. These modular software programs are controlled by a meta-system which manages the selection, operation, and communication of these programs. This new architecture can serve as a universal configuration to develop high-performance intelligent systems for many complicated application domains in the real-time manufacturing process. As an example, an intelligent optimal control is utilized to illustrate the integrated intelligent control system.     

An Interactive System SDI on Microcomputer

SDI is an interactive system,based on PASCAL,for Symbolic Differentiation and Integrationcompulation.It runs on an IBM-PC.Both input and output are symbolic mathematical expressions.It canmanipulate symbolic differentiation,symbolic integration,and algebraic simplification,etc.The languageand implementation of SDI will be presented in this paper.     

容错控制系统部件重要度计算的CAD算法

部件(如传感器或执行器)的失效将导致系统性能的下降甚至完全失效。因此,在设计容错控制系统时确定部件重要度是非常重要的。本文提出了部件静态和动态重要度,它们分别表示了部件失效对系统静态和动态性能的影响程度。借助仿真和矩阵转换的运算,本文提出了能同时计算m个部件静态和动态重要度的CAD算法,例子验证了该法的有效性。     

On the Probability of the Number of Solutions for the P4P Problem

This paper studies the multi-solution phenomenon for the perspective four point (P4P) problem from geometric and algebraic aspects. We give a pure geometric proof that the P4P problem could have up to five solutions. We also give a clear picture on how these five solutions could be realized. We prove that with probability one, the P4P problem has a unique solution which can be represented by a set of rational functions in the parameters. The simulant experiments show that to solve the P4P problem with the rational functions is stable and accurate. Xiao-Shan Gao is a professor in the Institute of Systems Science, Chinese Academy of Sciences. His research interests include: automated reasoning, symbolic computation, intelligent CAD, CAGD, and robotics. He was published over one hundred research papers, two monographs and edited four books or conference proceedings. Webpage: http://www.mmrc.iss.ac.cn/~xgao. Jianliang Tang received his PhD degree from Chinese Academy of Sciences in 2004. Currently, he is an assistant professor in SheZhen University. His research interests include camera calibration and symbolic computation.     

Symbolic analysis and design of control systems using Mathematica

Contemporary computer tools can generate a tremendous amount of numerical data so the user might easily lose insight into the phenomenon being investigated. Those who use powerful computer algebra systems must thoroughly understand the assumptions that underlie the software. In this paper, the role and importance of symbolic computation in control engineering and signal processing is exemplified. Real-life application examples are presented in which systems are symbolically solved and simulated with Mathematica. We introduce an original approach to algorithm development, system design and symbolic processing that successfully overcomes some problems encountered in the traditional approach. Benefits of symbolic methods and the role of computer algebra systems are highlighted from the viewpoint of both academia and industry.     

Challenges of Symbolic Computation: My Favorite Open Problems

The success of the symbolic mathematical computation discipline is striking. The theoretical advances have been continuous and significant: Gröbner bases, the Risch integration algorithm, integer lattice basis reduction, hypergeometric summation algorithms, etc. From the beginning in the early 1960s, it has been the tradition of our discipline to create software that makes our ideas readily available to scientists, engineers, and educators: SAC-1, Reduce, Macsyma, etc. The commercial viability of our system products is proven by Maple and Mathematica. Today’s user communities of symbolic computation systems are diverse: educators, engineers, stock market analysts, etc. The mathematics and computer science in the design and implementation of our algorithms are sophisticated. The research challenges in symbolic computation at the close of the twentieth century are formidable. I state my favorite eight open problems in symbolic computation. They range from problems in symbolic/numeric computing, symbolic algorithm synthesis, to system component construction. I have worked on seven of my problems and borrowed one from George Collins. I present background to each of my problems and a clear-cut test that evaluates whether a proposed attack has solved one of my problems. An additional ninth open problem by Rob Corless and David Jeffrey on complex function semantics is given in an appendix.     

一种混合高性能计算机代数环境模型

提出一种高性能计算机代数环境HHPCAS,综合现有的多种计算机代数软件,通过添加内核扩展函数、外部调用等方法,结合集群管理软件和并行环境,可以提供高性能的计算机代数计算环境。HHPCAS根据Slot/Ticket模型可以有效管理可用计算资源和作业优先等级,充分发挥多种计算机代数软件的特长,并且提供并行的消息传递机制,将大量复杂的计算平均分配到每个计算节点,解决单台机器内存受限和计算能力有限等问题。通过并行差分代换方法测试表明HHPCAS可以为符号计算和计算机自动推理提供有效的计算平台。     

基于符号神经网络的数据溶合系统的研究

本文介绍一种把多个神经网络和符号推理结合在一起用于移动式机器人多传感器数据溶合的新技术。用该技术实现的系统不仅能够准确定位，而且可以增强机器人的应变能力。     

Graphical reasoning in compact closed categories for quantum computation

Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for reasoning about compact closed categories. A salient feature of our system is that it provides a formal and declarative account of derived results that can include ‘ellipses’-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.     

Special issue on the use of computer algebra systems for computer aided control system design

The importance of the continuing and growing need in the systems and control community for reliable algorithms and robust numerical software for increasingly challenging applications is well known and has already been reported elsewhere (IEEE Control Systems Magazine, Vol. 24, Issue 1). However, we have all had the experience of working on a mathematical project where an increased number of symbolic manipulations was needed. In a simple case, the required computation might have been to compute the Laplace transform or the inverse Laplace transform of a function, or to find the transfer function matrix for a given system topology where parameters are included. In a more demanding situation the required computation might have been to find the parametric family of solutions of a polynomial matrix Diophantine equation resulting from a variety of control problems such as those associated with stabilization, decoupling, model matching, tracking and regulation, or to compute the Smith McMillan form of a rational transfer function matrix in order to obtain a better insight into a number of structural properties of a system. The desire to use a computer to perform long and tedious mathematical computations such as the above led to the establishment of a new area of research whose main objective is the development: (a) of systems (software and hardware) for symbolic mathematical computations, and (b) of efficient symbolic algorithms for the solution of mathematically formulated problems. This new subject area is referred to by a variety of terms such as symbolic computations, computer algebra, algebraic algorithms to name a few. During the last four decades this subject area has accomplished important steps and it is still continuing its evolution process.     

Symbolic finite element analysis using computer algebra: Heat transfer in rectangular duct flow

The problem of heat transfer in fully developed laminar flow in a rectangular duct is solved using a symbolic finite element method. The Nusselt number is obtained as a power series of the aspect ratio of the duct. The solution procedure here differs from the conventional finite element method, in that the aspect ratio remains in symbolic form throughout the computation. Part of the computation is done using the computer algebra system Mathematica. However, the most computational intensive part which involves a Gauss elimination in symbolic form is implemented using an ordinary computer program without resorting to a computer algebra system. The agreement between the results from the present work and those from exact numerical procedures is reasonable.     

Symbolic control of linear systems based on symbolic subsystems

This paper describes an approach to the control of continuous systems through the use of symbolic models describing the system behavior only at a finite number of points in the state space. These symbolic models can be seen as abstract representations of the continuous dynamics enabling the use of algorithmic controller design methods. We identify a class of linear control systems for which the loss of information incurred by working with symbolic subsystems can be compensated by feedback. We also show how to transform symbolic controllers designed for a symbolic subsystem into controllers for the original system. The resulting controllers combine symbolic controller dynamics with continuous feedback control laws and can thus be seen as hybrid systems. Furthermore, if the symbolic controller already accounts for software/hardware requirements, the hybrid controller is guaranteed to enforce the desired specifications by construction thereby reducing the need for formal verification.     

可能性测度下的CTL符号化模型检测

随着系统复杂性的增加,系统中的不确定信息亟待处理,状态爆炸问题也越来越严峻,现有的模型检测技术已不能完全适用于复杂系统的验证。 对可能性测度下CTL符号化模型检测进行了研究。首先用多终端二值决策图和布尔公式分别描述系统模型和待验证性质,然后再对系统模型进行归一化和简化,最后利用不动点计算完成系统验证。该研究是对可能性测度下的模型检测技术和符号化模型检测技术的整合,不但能处理系统的不确定信息,而且保持了符号化模型检测对计算时空要求低的优点,对于复杂系统模型检测具有重要意义。     

Grid-Oriented Computation: Integrated Library GridComp

An approach to expedite the computation of functions on grids is discussed. The GridComp integrated library developed by the author is described. This library is based on the combined use of symbolic and numerical means, which makes it possible to expedite such computations. The library can be used in C and C++ codes and in the computer algebra system Maple.     

一种新型计算机代数系统编译器的设计与实现

计算机代数系统（Computer Algebra System,CAS）是集大整数运算和符号运算于一体的计算平台,这方面的代表软件有Maple和Mathematica。然而,在计算机代数系统的设计中,编译器的设计与实现始终是一个关键和难点。GiNaC是Linux平台上开放源码的符号计算包,该文以它为基础提出了一种新型CAS编译器的设计方法,并在Linux平台上实现。新的CAS编译器兼容Maple编程语言, 对比测试结果显示它的效率并不逊色于Maple。     

Symbolic computation of nonlinear wave interactions on MACSYMA

In this paper we describe the use of a large symbolic computation system - MACSYMA - in determining approximate analytic expressions for the nonlinear coupling of waves in an anisotropic plasma. MACSYMA was used to implement the solutions of a fluid plasma model nonlinear partial differential equations by perturbation expansions and subsequent iterative analytic computations. By interacting with the details of the symbolic computation, the physical processes responsible for particular nonlinear wave interactions could be uncovered and appropriate approximations introduced so as to simplify the final analytic result. Details of the MACSYMA system and its use are discussed and illustrated.