Symbolic-numeric interface: A review

A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach

Uses Made of Computer Algebra in Physics

Computer algebra is a tool building activity. This paper is a review of acceptance of this tool by physicists and theoretical chemists during the period from the EUROSAM-79 survey to the Spring of 1988, as reflected by the literature which quotes computer algebra. After considering the traditional areas of application; celestial mechanics, relativity and quantum mechanics, we extend our examination to other areas of physics which would appear, from the literature, to be using computer algebra efficiently: fluid mechanics, plasma physics, optics, perturbation technology, continuum mechanics, numerical analysis for physics, mechanics, non-linear evolution equations, theoretical chemistry and other applications

Design and implementation of a language for manipulating algebraic formulae

This thesis explores the possibilities of doing mathematical problems involving algebra on a computer. A language is designed which allows names to occur as unknown quantities. This language has all the facilities of a general purpose language such as IMP, but is designed to be used inter-actively by a user at a console. The language also includes instructions which cause the usual algebraic operations to be applied to expressions. These operators include simplification, differentiation, but not integration. A brief survey is given of other languages in the field, with comments on their capabilities and restrictions. The second part of the thesis describes how the language is implemented. An interpreter is used. Statements of the language are analysed syntactically and then obeyed. Algebraic expressions are stored in byte arrays, using a type of prefix Polish notation. Finally the language is reviewed in the light of recent work done in the field, and suggestions are made for a further version

Corporate governance and profit manipulation: a French field study

Profit manipulation has been largely studied through Positive Accounting Theory (PAT). However, the weakness of the results obtained would suggest using different theoretical and methodological approaches to examine this subject. In France, management controllers play a central role in profit manipulation. This paper offers a comprehensive analysis of their profit manipulation practices. Using results from 32 interviews in 13 companies, we argue that the spread of Anglo-Saxon corporate governance model has fostered such behaviour. Far from the opportunism hypothesis supported by Positive Accounting Theory, profit manipulation is used as a tool by management controllers to gain broader legitimacy within organisations and/or to adopt what they claim to be ethical behaviour.profit manipulation; management controllers; corporate governance; field study

Application of symbolic and algebraic manipulation software in solving applied mechanics problems

As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role

High Performance Sparse Multivariate Polynomials: Fundamental Data Structures and Algorithms

Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit a sparse arithmetic scheme introduced by Johnson in 1974, adapting and optimizing these algorithms for modern computer architectures, with our implementations over the integers and rational numbers vastly outperforming the current wide-spread implementations. We develop a new algorithm for sparse pseudo-division based on the sparse polynomial division algorithm, with very encouraging results. Polynomial interpolation is explored through univariate, dense multivariate, and sparse multivariate methods. Arithmetic and interpolation together form a solid high-performance foundation from which many higher-level and more interesting algorithms can be built

Data structures for algebraic manipulation

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Analytical differentiation by computer using a Symmetrical List Processor

The Symmetrical List Processor SLIP; developed by Professor Joseph Weizenbaum of MIT, was implemented with considerable modifications and additions on the University of Cape Town computer. A package to perform automated analytical differentiation (DERIV) was developed using SLIP. Basic simplification techniques as well as convenient input and output routines were included. The package was tested extensively and a rough comparison drawn with the abilities of various computer languages and programs which include the same facility as TIERIV

Clinician empathic speech and client change language : is there an association between empathic speech and change talk in motivational interviewing sessions?

Empathy is the state of knowing or being aware of another persons perspective and the ability to express empathy is acknowledged as an important component within effective psychotherapy. Motivational interviewing (MI) is a specific method of psychotherapy in which clinician expressions of empathy are held to be an active ingredient and a central component of effective practice. Although empathy has long been a part of the theoretical explanation of effective MI, there is little known about the function of empathy as expressed by the clinician and the association between such in-session speech and client change language. This study identified the empathic speech of clinicians and explored the association of such speech with client change language. The study found that frequencies of empathic speech shared a significant positive correlation with client change talk as well as client sustain talk. This correlation between empathic speech and change talk was mediated by several clinician variables, such as MI-consistent behaviors and clinician reflections of client change talk. Similarly, the relationship between empathic speech and client sustain talk was mediated by reflections of client sustain talk