Norbert Kajler

CAS/PI: a portable and extensible interface for computer algebra systems

CAS/7T is a Computer Algebra System graphic user interface designed to be highly portable and extensible. It has been developed by composition of pre-existing software tools such as Maple, Sisyphe, or Ulysse systems, ZicVis 3-D plotting library, etc, using control integration technology and a set of high level graphic toolkits to build the formula editor and the dialog manager. The main aim of CAS/71_ is to allow a wide range of runtime reconfiguration and extensions. For instance, it is possible to add new tools to a running system, to modify connections between working tools, to extend the set of graphic symbols managed by the formula editor, to design new high level editing commands based on the syntax or semantics of mathematical formulas, to customize and extend the menu-button based user interface, etc. More generally, CAS/7T can be seen equally as a powerful system-independent graphic user interface enabling inter-systems communications, a toolkit to allow fast development of custom-made scientific software environments, or a very convenient framework for experimenting with computer algebra systems protocols and man-machine interfaces.

A Survey of User Interfaces for Computer Algebra Systems

This 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.

Building a Computer Algebra Environment by Composition of Collaborative Tools

Building a software environment for Computer Algebra is quite a complex issue. Such an environment may include one or more Symbolic Computation tools, some devices, such as plotting engines or code generators, and a way to link others scientific applications. It is also expected that any of these components may be run on a remote processor and that the whole system is used via a convenient graphical user interface. The natural extensibility of Computer Algebra software, as well as the diversity of the needs expressed by their users, necessitate a highly open and customizable software architecture allowing different kinds of extensions and adaptations. Our approach consists of building the environment by composition of separately developed packages, using state of the art software engineering technologies in the spirit of the tool integration paradigm. This way, the different software components should be able to exchange data and freely cooperate with each other, without being too tightly coupled as in a monolithic system. A prototype of such an environment is currently under development in the framework of the SAFIR project. It will be built using an implementation of the software bus concept developed for the next version of Centaur, and should include a set of components, developed both internally and externally, and a homogeneous user interface.

Design and Implementation of MP, a Protocol for Efficient Exchange of Mathematical Expressions

The Multi Project is an ongoing research effort at Kent State University aimed at providing an environment for distributed scientific computing. An integral part of this environment is the Multi Protocol (MP) which is designed to support efficient communication of mathematical data between scientifically-oriented software tools. MP exchanges data in the form of linearized annotated syntax trees. Syntax trees provide a simple, flexible and tool-independent way to represent and exchange data, and annotations provide a powerful and generic expressive facility for transmitting additional information. At a level above the data exchange protocol, dictionaries provide definitions for operators and constants, providing shared semantics across heterogeneous packages. A clear distinction between MP-defined and user-defined entities is enforced. Binary encodings are used for efficiency. Commonly used values and blocks of homogeneous data are further optimized. The protocol is independent of the underlying communication paradigm and can support parallel computation, distributed problem-solving environments, and the coupling of tools for specific applications.

From honest to intelligent plotting

Adaptive and honest plotting are two techniques to improve the quality of curve and surface visualization packages. Beyond honest plotting, we investigate a number of alternative techniques in order to improve correctness and completeness of 2D and 3D plotting, increase efficiency, and achieve better usability. We refer to these techniques as intelligent plotting as most of them transparently take advantage of the numerical and/or symbolic capabilities available from some mathematical engine in order to provide better and faster graphical displays. We implemented these techniques inside two very different packages: the Graphing Calculator and IZIC which we used as testbeds for our experiments.

Visualization of mathematical surfaces: the IZIC server approach

Abstract This paper presents IZIC, a stand-alone high-quality 3D graphic tool driven by a command language. IZIC is an interactive version of ZICLIB , a 3D graphic library allowing efficient curve and surface manipulations using a virtual graphic device. Capabilities of ZICLIB include management of pseudo or true colors, illumination model, shading, transparency, etc. As an interactive tool, IZIC is run as a Unix server which can be driven from one or more computer algebra systems, including Maple, Mathematica, Macsyma, and Reduce, or through an integrated user interface such as CAS/PI. Connecting IZIC with a different system is a very simple task which can be achieved at run-time and requires no compilation. Also important is the possibility to drive IZIC both through its freely-reconfigurable menu-button user interface, and through its command language. This brings a high level of programmability and interoperability, allowing, for instance, the remote animation of surfaces from the symbolic computation engine.

Pluggability Issues in the Multi Protocol

There are several advantages to providing communication links between independent scientific applications. Important problems to solve include data and control integration. Solving these problems separately is an essential aspect of the design and implementation of a protocol for mathematics. The Multi Protocol (MP) specification addresses the exchange of mathematical data by focusing only on the data encoding issues. In this way, MP can be plugged into various existing data transport mechanisms addressing control integration, or augmented by a higher control-related protocol layer. Our implementation of MP is independent of the data transport mechanism and can work with several devices. An application puts/gets data to/from MP buffers which communicate with the transport device through an abstract device interface. This paper describes the general design of the interface between MP and a transport device and the lessons we have learned during its implementation.

Some human interaction issues in computer algebra

This paper addresses some of the current issues concerning the improvement of user interfaces for computer algebra systems. Some state of the art commercial software as well as research prototypes are presented, followed by a description of present research directions.

User interfaces for symbolic computation: a case study

Designing user interfaces for Symbolic Computation tools like Maple, Mathematical, Reduce, etc, implies solving some challenging difficulties, including the display and manipulation of mathematical formulas, efficient and user-friendly manipulation of possibly large expressions, deep extensibility y of the user interface, etc. This also implies dealing with some complex communication issues in order to efficiently integrate under a common user interface a set of tools from different origins running across a distributed architecture. This includes transparent management of remote comput ations, hiding command language variations, and programmability of the whole environment so that one can solve complex problems by sequentially and/or concurrently applying any needed tools. Very few of these problems are addressed by the user interfaces of commercially available packages. To improve user interfaces and integration of Symbolic Computation tools, a prototyping system named CAS/PI has been implemented. Its main characteristics are to be highly flexible and extensible, and to be based on pre-existing software engineering technologies. Using CAS/PI, each of the previously stated problem may be solved in a generic way, allowing further experiment ations and optimization.

The Internet accessible mathematical computation framework

The Internet Accessible Mathematical Computation (IAMC) framework aims to make it easy to supply mathematical computing powers over the Internet/Web. The protocol-based IAMC framework enables developers to create interoperable clients and servers easily and independently. Presented are conceptual and experimental work on the IAMC framework architecture and major components: the Mathematical Computation Protocol (MCP), a client prototype (Dragonfly), a server prototype (Starfish), a mathematical encoding converter (XMEC), and an open mathematical compute engine interface (OMEI).