Kostas Zotos

Performance comparison of Maple and Mathematica

Abstract There are two major, widely available, symbolic mathematical computer systems: Maple and Mathematica. Both have recent new versions with Mathematica 5.2 and Maple 10, the latter being a major upgrade. The packages have extensive similarities in the computational work they’re intended to support. In this paper my goal is to help you decide which of them is better suited to your temperament or your current technological practice. I donot intend to try to prove, and will not assert, that one package is better than another. Rather, my methodology is intended to present a basis for each reader to create a personal metric for comparing the packages.

Computer Algebra Systems – New strategies and techniques

Software engineers require systematic approaches in order to develop complex large-scale systems and to integrate and migrate existing solutions. Also they need techniques to improve the software reliability, maintainability, performance and dependability, and methodological support to manage the development process effectively and productively. Computer algebra systems are software packages, usually Object-oriented, which are used in manipulation of mathematical formulas. The primary goal of a Computer Algebra System (CAS) is to automate tedious and sometimes difficult algebraic manipulation tasks. The specific uses and capabilities of these systems vary greatly from one system to another. Some of them include facilities for graphing equations and provide a programming language for the user to define their own procedures. In this paper we are going to examine new design strategies and techniques.

Object-oriented programming in Mathematics

Abstract The entire mathematical software engineering process should be driven by the need to build products that conform to their requirements, and to demonstrate, as early in the development cycle as possible, the quality of each component. Quality cannot be tested into a product; it must be built in from the start. Furthermore, mathematical software engineers should follow some rules in order to achieve the accuracy, modularity, deferred commitment, reusability and naturalness. It’ astonishing simple to implement complex mathematical algorithms in unstructured programming but it’s harmful to “reinvent the wheel” every time you create a program. In this paper, I am going to examine the importance of Object-orientated programming in Mathematics.

Object-oriented design principles in mathematics

Abstract It is astonishingly simple to implement complex mathematical structures into an object-oriented environment, but it is harmful to “reinvent the wheel” every time you create a program. Furthermore, you should follow some rules in order to achieve accuracy, modularity, deferred commitment, reusability and naturalness. In this paper, I am going to present some object-oriented design principles to solve the “software crisis” between “pure mathematics” and computer science.

Improving numerical software

Abstract Traditionally there have been two opposite theories in software engineering. The first is that users want “black box” software that they can use with complete confidence for general problem classes without having to understand the fine algorithmic details. The second is that users want to be able to tune data structures for a particular application, even if the software is not as reliable as that provided for general methods. It turns out both are true, for different groups of users. Traditionally, users have asked for and been provided with “black box” software in the form of mathematical libraries such as LAPACK, LINPACK, NAG, and IMSL. More recently, the high-performance community has discovered that they must write custom software for their problem. Their reasons include inadequate functionality of existing software libraries, data structures that are not natural or convenient for a particular problem and overly general software that sacrifices too much performance when applied to a special case of interest. Can we improve numerical libraries? The answer is yes and we are going to investigate in this paper some methods.