A Survey of User Interfaces for Computer Algebra Systems

AbstractThis paper surveys work within the Computer Algebra community (and elsewhere) directed towards improving user interfaces for scientific computation during the period 1963–1994. It is intended to be useful to two groups of people: those who wish to know what work has been done and those who would like to do work in the field. It contains an extensive bibliography to assist readers in exploring the field in more depth. Work related to improving human interaction with computer algebra systems is the main focus of the paper. However, the paper includes additional materials on some closely related issues such as structured document editing, graphics, and communication protocols

The design of a user interface to a computer algebra system for introductory calculus

We are developing a unique computational environment for use in conjunction with the two-semester introductory calculus sequence. Our system, called Newton (formerly The Calculus Companion), runs on Macintosh computers and consists of a user-friendly interface to the symbolic mathematics package Maple, supplemented by an extensive library of our own Maple code. Formulas are easily constructed and modified, appearing exactly as they do in textbooks; multiple windows allow users to see and work with several formulas at once. Formulas, graphs, and text can be intermixed on worksheets. Users do not interact with Maple directly and need know nothing of Maple\u27s syntax and command structure. Mathematical operations are selected from menus, with the added bonus that this makes it possible to document solutions. In addition, dialogs have been constructed to illustrate computational methods such as the chain rule for differentiation and integration by parts. As part of the project, we have also developed an interactive package for two-dimensional plotting that allows users to manipulate graphs of functions rather than merely view them as static objects. The system additionally contains an intelligent tutor that can assist users in solving problems on techniques of integration. The software enables students to concentrate on learning the important concepts of calculus, guiding them through complex problem solving requiring multiple steps, and freeing them from boring and error-prone calculations. The computer thereby encourages creativity through rapid feedback and experimentation, making the exploration of mathematics more exciting and enjoyable