Marc Gaëtano

An OpenMath 1.0 implementation

The first official version of the OpenMath specification was released in December. This paper presents the first implementation of this standard, in the form of a C library. To ensure a faithful realization, a second, independent implementation with the same api was built using Aldor (A). We describe how the C library has been embedded in two main-stream computer algebra systems, Maple and Reduce, which can now communicate with each other and Aldor, and with specialized programs also linking the libraries. We discuss some of the problems encountered in developing the api, and the solutions we have chosen.

A Deductive Database for Mathematical Formulas

In this paper, we present mfd2, a deductive database for mathematical formulas. The database itself is a stand-alone program which can run as a server in a client/server environment and it has been designed to be a powerful assistant for computer algebra systems as well as for other applications. For example, mfd2 could be used in an electronic handbook of mathematical relations or as a lemma database for a theorem prover. The information stored in the database is accessed through a specialized query language. At the heart of mfd2 is a deduction engine based on an algorithm for associate-commutative unification that takes care of the conditions associated with the formulas.

Making Systems Communicate and Cooperate: The Central Control Approach

In this paper we present the Central Control, a software component designed to be the kernel of environments for scientific computation and which can offer a common and concurrent access to many tools needed by the scientist and the engineer. The Central Control (often abbreviated as CC in the sequel) communicates with servers that can be general purpose or specialized computer algebra systems, numerical systems, visualization programs, graphical interfaces etc. The Central Control can abstract the syntaxic and semantic differences of the systems so that, for example, an expression computed by Mathematica can be used as input to Maple. The CC is in fact an extended Scheme interpreter. This enables the dynamic configuration of a network of servers to distribute computations using the full power of the Scheme language. Architectures which support the solution of mathematical problems by linking specialized components are important to the future growth of Computer Algebra. The CC is a tool designed to make experiments in this direction easily. It has been used to build an efficient library for computational algebraic geometry. This library has been used to implement a new algorithm for primary decomposition of ideals.

A distributed and cooperative environment for computer algebra

Abstract In this paper, we describe the Central Control , a software component that enables several symbolic systems to cooperate and exchange data. The Central Control has been designed to be the kernel of an environment for scientific computations which can offer a common and concurrent access to several tools needed by the scientist and the engineer: general purpose and specialized computer algebra systems, visualization tools, links with numerical libraries and tools to manipulate numerical programs etc . The user can interact with the Central Control through one or more (graphical) user interfaces. The Central Control achieves its goals by requiring as little as possible from the tools and by using a particular programming language to provide a unified view for the objects and the operations performed by the connected tools. The Central Control will be used as the basis of the Comprehensive Solver that will provide common access to all the programs developed within the POSSO ESPRIT/BRA project. We give a simple example of an actual use of the Central Control for computing primary decompositions of ideals.

Decision Support System Architecture for Real-Time Water Management

Management of water uses requests to harmonize demands and needs which are getting more and more complex and sophisticated. During the past three decades, modeling systems for hydrology, hydraulics, and water quality have been used as stand-alone products and were used in order to produce an analysis of a current situation and to generate forecast according to different horizons. The current situation, characterized by the fast increase of monitoring devices mainly in urban environments, requests an integration of the modeling tools into the information systems that are now dedicated to the global management of urban environments and related services. Energy distribution, water distribution, solid wastes collection, and traffic optimization are today major issues for cities that are looking for functional Decisions Supports Systems (DSSs) that may integrate the various components and operate in a sustainable perspective. In addition, the basic requirement of real-time assessment of the situation, the modeling systems identified as main elements of analytics and used for hydrology, hydraulic, and water quality forecasts have to integrate a common framework allowing modular approach and interoperability. This chapter presents the interest for a generic operational approach that could be implemented in order to address the management of water uses in a complex urban environment and to provide real-time assessment and forecasts. The proposed approach is illustrated with the AquaVar project, an application developed on the Var catchment located in the French Riviera and for an area of 3000 km2.

Mathematical Services Composition

This paper describes the definition and the use of a plan language in the context of mathematical web services. A plan is a document intended to describe how to use different mathematical web services to solve a particular problem. A plan is like a program in which most of the function calls have to be handled by web services. A plan is a multiple-state choreography document which could be either abstract, unresolved or resolved, depending on how much of the web services involved in the choreography is known. Such a plan can be instantiated into a composition language such as BPEL or to a mathematical routine (like a Maple routine) for execution.

Mathematical Web Services: A Case Study

This paper presents a attempt to use the semantic web technologies to deploy and interact with a mathematical package called Bernina. This work is carried out within a European Union funded project called MONET aiming at demonstrating the application of the latest ideas for creating a semantic web to the world of mathematical software. While many of these ideas address the general problem of delivering online web services, they need to be tailored to suit mathematical services. After a brief overview of Bernina we focus on the problem of mathematical services discovery and describe the broker, a key component in the MONET framework. In order to register to a broker, a mathematical service should be able to describe the problem it is intended to solve. We discuss the ontology and taxonomy aspects of the project and show on a small example how it could be used to describe Bernina functions. Before some concluding remarks, we present our prototype implementation of Bernina as a mathematical web service.

Design of a customizable component to display and edit formulas

This paper describes the design and implementation of Emath, a highly customizable component t.0 displ+and edit mathematical formulas. Ema th has been designed to be embedded in other applications and uses a Lisp dialect. as its cstension language in the same spirit as t.he Emacs t,est editor. ‘To ensure responsivcncss, the cdit.or is multi-t.hrcadcd and normally runs AS il SepXilte process.

Algorithm animation with Agat

Algorithm animation is a powerful tool for exploring a program’s behavior. It is used in various areas of computer science, such as teaching (Rasala et al. 1994), design and analysis of algorithms (Bentley and Kernighan 1991), performance tuning (Duisberg 1986). Algorithm animation systems provide a form of program visualization that deals with dynamic graphical displays of a program’s operations. They offer many facilities for users to view and interact with an animated display of an algorithm, by providing ways to control through multiple views the data given to algorithms and their execution.