Macsyma: A personal history

AbstractThe Macsyma system arose out of research on mathematical software in the AI group at MIT in the 1960s. Algorithm development in symbolic integration and simplification arose out of the interest of people, such as the author, who were also mathematics students. The later development of algorithms for the GCD of sparse polynomials, for example, arose out of the needs of our user community. During various times in the 1970s the computer on which Macsyma ran was one of the most popular nodes on the ARPANET. We discuss the attempts in the late 70s and the 80s to develop Macsyma systems that ran on popular computer architectures. Finally, we discuss the impact of the fundamental ideas in Macsyma on the author’s current research on large scale engineering and socio-technical systems

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

Mission and data operations IBM 360 user's guide

The M and DO computer systems are introduced and supplemented. The hardware and software status is discussed, along with standard processors and user libraries. Data management techniques are presented, as well as machine independence, debugging facilities, and overlay considerations

The design and implementation of a tutorial program to perform symbolic mathematics

The purpose of this thesis is to design and implement a program that could be used for a drill in symbolic mathematics. The scope of the program with respect to the range of problems that it solves is limited to selected types from elementary algebra, trigonometry, differential calculus, and integral calculus. The program is designed, not only to give solutions (answers), but also to provide several of the intermediate steps leading to the final result. FORMAC73 and PL/1 are used to implement the program. FORMAC73 is a system and a language for manipulating mathematical expressions, symbolically. The facilities of PL/1 are available for program structure, loop control, testing, input and output operations, and manipulating the strings so as to get the intermediate steps. The program is designed to provide supplementary assistance to give students drill, practice, and review several specific topics in the stated areas. The program may also be used by instructors to check or to provide answers to particular problems, say for an examination or homework. The program does not attempt to diagnose the student‘s difficulties. The main accomplishments of this paper will be to show the potential of using FORMAC73 with the existing facilities at Virginia Commonwealth University (VCU) to develop an extensive tutorial drill; particularly in arithmetic and algebra. The paper will also show that it is possible to develop a comprehensive CAI package in symbolic mathematics by using existing symbolic mathematics systems

Programming Langauges: A short history for economists

The development of programming languages as a means of communicating with digital computers is surveyed with emphasis on those languages and characteristics of particular relevance to economists and statisticians. There are several different types of software: (1) True programming languages which are used for many purposes in communicating with the machine, such as FORTRAN. (2) Software with greater specificity in purpose and function such as MATHEMATICA, GAUSS, MATLAB and MAPLE. (3) "Libraries" or collections of special purpose algorithms designed to be used within programs written in one of the major languages, e.g., the LINPACK, MINPACK, EISPAC, and IMSL libraries. (4) Collections of programs, sometimes called packages, linked together and designed for special purposes. These generally must be used within some of the languages one step removed from the basics. Examples include MATLAB Toolboxes. (5) Finally, there are programs which although made generally available cannot be used stand-alone in any sense

Data structures for algebraic manipulation

Imperial Users onl

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

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