Maple programming guide

Springer eBooks, 1992

Library of Congress Caltaloging-in-Publication Data First Leaves: a tutorial introduction to Maple V / Bruce W. Char ... let aLl. p. em. Includes bibliographical references and index. 1. Maple (Computer program) 2. Algebra-Data processing. 1. Char, Bruce W. QA155.7.E4556 1992 510'" .285' 369-dc20 91-47590 CIP Maple is a registered trademark of Waterloo Maple Software.

Special Talk, 2019

* Introduction - Expressions - Functions * Solving Equations - Solutions of Equations - Solving a System of Equations for Several Unknowns - Solving Differential Equations * Plotting - Three-dimensional plotting - Create a 2-D or 3-D animation on one parameter * Procedures, Variables, and Extending Maple * Sample Programming - Fibonacci Series - Applications of Bisection Method - New Root-Finding Algorithm * Maple Help * References

Studies have shown that good comments can help programmers quickly understand what a method does, aiding program comprehension and software maintenance. Unfortunately, few software projects adequately comment the code. One way to overcome the lack of human-written summary comments, and guard against obsolete comments, is to automatically generate them. In this paper, we present a novel technique to automatically generate descriptive summary comments for Java methods. Given the signature and body of a method, our automatic comment generator identifies the content for the summary and generates natural language text that summarizes the method's overall actions. According to programmers who judged our generated comments, the summaries are accurate, do not miss important content, and are reasonably concise.

2006

We wish to answer the following question: what is the most appropriate language for describing the "contracts" that Maple routines offer? In this, we are seeking much more than types (which Maple does not have, at least statically), as these are not sufficiently expressive to capture what is going on. We also wish to study what is actually in Maple, rather than what should be there. Put another way, we do not expect to find that a type system like Aldor's or Axiom's would be especially helpful in explaining Maple. Our real goal is a mathematical description of the interfaces between routines. As such, the only current terminology flexible enough to encompass reality is that of contracts, by which we mean simply statements of complex properties (static as well as dynamic) in a sufficiently general logic.

2018

In this chapter we explore the ways to create a function and a loop in Python. We may need to create a loop to iterate an action over a list, or to create a function to extract some cases from a dataset. Writing functions is very important to automating data analysis.

2010 Annual Conference & Exposition Proceedings

The information contained in this paper is of an introductory nature a tutorial on the 'Maplet Development and Programming' for selected science and engineering students. The knowledge gained by the authors is documented here to help students who are interested in pursuing science and/or engineering for their degree, and who have a keen interest in a hands-on experience for solving selected science/engineering problems using MAPLE. As a part of this tutorial, technical how-to details are given to help the student develop simple maplets with simple programming constructs that are needed to solve these selected problems. The process of developing Maplets demonstrated within this tutorial will provide a hands-on experience using MAPLE. The authors believe that this paper will engage engineering and science students to create or modify existing Maplets for their other college course activities. The tutorial assumes a familiarity with basic programming constructs, and would be appropriate after an introductory programming course, one year of the calculus and one year of any physical science.

Information Processing Letters

Various proof rules for procedure calls in weakest precondition semantics have been proposed. The author gives a proof rule that is very easy to use, but does not yield the best possible answer for every specification – only for a large class of specifications called normal specifications. In the Appendix, he shows how every specification can be transformed into an equivalent normal one.

Programming Languages and Systems, 2007

We describe a new technique for computing procedure summaries for performing an interprocedural analysis on programs. Procedure summaries are computed by performing a backward analysis of procedures, but there are two key new features: (i) information is propagated using "generic" assertions (rather than regular assertions that are used in intraprocedural analysis); and (ii) unification is used to simplify these generic assertions. We illustrate this general technique by applying it to two abstractions: unary uninterpreted functions and linear arithmetic. In the first case, we get a PTIME algorithm for a special case of the long-standing open problem of interprocedural global value numbering (the special case being that we consider unary uninterpreted functions instead of binary). This also requires developing efficient algorithms for manipulating singleton context-free grammars, and builds on an earlier work by Plandowski [13]. In linear arithmetic case, we get new algorithms for precise interprocedural analysis of linear arithmetic programs with complexity matching that of the best known deterministic algorithm [11].

ACM Transactions on Programming Languages and Systems, 1980

The multiple assignment statement is defined in full generality—including assignment to subscripted variables and record fields—using the “axiomatic” approach of Hoare. Proof rules are developed for calls of procedures using global variables, var parameters, result parameters, and value parameters, using the idea of multiple assignment to provide understanding. An attempt is made to clarify some issues that have arisen concerning the use of rules of inference to aid in generating “verification conditions” in mechanical verifiers and the use of logical variables to denote initial values of program variables.

Audiovisual communication review, 1962

2002

Advanced Mathematical Methods with Maple During the past five years there has been an immense growth in the use of symbolic computing and mathematical software packages, such as Maple, which provide an invaluable tool for mathematicians and physical scientists alike. ...

1978

The presence of procedures and procedure calls in a programming language can give rise to various kinds of side effects. Calling a procedure can cause unexpected references and modifications to variables (variable side effects) and non-obvious transfers of control (exit side effects). In addition procedure calls and parameter passing mechanisms can cause several different variable names to refer to the same location thus making them aliases. This in turn causes all of these variables to be accessed whenever one of the variables is modified or referenced. Determining the aliases of variables and the exit and variable side effects of procedure calls is important for a number of purposes including the generation of optimized code for high level languages. This paper presents a method of determining exit and variable side effects and gives an algorithm for determining the aliases of variables. The principal advantage over previous methods is that only one pass over a program is used to ...

2003

ACM SIGCSE Bulletin