Wolfgang Schreiner

Distributed maple: parallel computer algebra in networked environments

We describe the design and use of Distributed Maple, an environment for executing parallel computer algebra programs on multiprocessors and heterogeneous clusters. The system embeds kernels of the computer algebra system Maple as computational engines into a networked coordination layer implemented in the programming language Java. On the basis of a comparatively high-level programming model, one may wrate parallel Maple programs that show good speedups in medium-scaled environments. We report on the use of the system for the parallelization of various functions of the algebraic geometry library CASA and demonstrate how design decisions affect the dynamic behaviour and performance of a parallel application. Numerous experimental results allow comparison of Distributed Maple with other systems for parallel computer algebra.

The design of the SACLIB/PACLIB kernels

This paper describes the design of the kernels of two variants of the SAC-2 computer algebra library: Saclib and Paclib. Saclib is a C version of SAC-2, supporting automatic garbage collection and embeddability. Paclib is a parallel version of Saclib, supporting lightweight concurrency, non-determinism, and parallel garbage collection.

A Web registry for publishing and discovering mathematical services

This paper describes an extension of the ebXML registry for publishing and discovering mathematical service descriptions. The MathBroker registry is able to handle descriptions given in the mathematical service description language, a language designed ad-hoc for capturing the semantics of Web services dealing with mathematical problems. The registry is distributed with a Java API implementing a MathBroker specific JAXR provider.

A Lightweight MDSD Process Applied in Small Projects

Model driven software development, domain specific languages and other generative programming approaches have gained much attention. There is a large number of tools available, starting from simple code generators to full-blown tool suites. There are several success stories and process frameworks about applying full scale MDSD approaches, but there is no or little help for small-size projects. To fill this gap, we designed a new development process which targets small and middle size projects with limited resources. According to our experience the process is working efficiently in small projects even if they cannot afford bigger initial resource investment. In this experience report we document an industrial project in which the process was used. We present this process in the form which is applied in the first project and also discuss our experience and the limitations of the process.

The Design of the PACLIB Kernel for Parallel Algebraic Computation

This paper describes the runtime kernel of Paclib, a new system for parallel algebraic computation on shared memory computers. Paclib has been developed as a professional tool for the simple design and efficient implementation of parallel algorithms in computer algebra and related areas. It provides concurrency, shared memory communication, non-determinism, speculative parallelism, streams and a parallelized garbage collection. We explain the main design decisions as motivated by the special demands of algebraic computation and give several benchmarks that demonstrate the performance of the system. Paclib has been implemented on a Sequent Symmetry multiprocessor and is portable to other shared memory machines and workstations.

A Para-Functional Programming Interface for a Parallel Computer Algebra Package☆

Abstract We describe the application of pD, a small para-functional language that we developed as a high-level programming interface for the parallel computer algebra package PACLIB. pD provides several facilities to express parallel algorithms in a flexible way on different levels of abstraction. The compiler translates a pD module into statically typed parallel C code with explicit task creation and synchronization constructs. This target code can be linked with the PACLIB kernel, the multi-processor runtime system of the computer algebra library SACLIB. The parallelization of several computer algebra algorithms on a shared memory multi-processor demonstrates the elegance and efficiency of this approach.

Querying Registry-Published Mathematical Web Services

This paper describes a light-weight, content-based, functional query language. The mathematical services query language (MSQL) has been developed for querying mathematical Web services described in the mathematical services description language (MSDL) and published in the MathBroker registry. Based on a client query, MSQL uses the registry to retrieve a candidate collection of documents and then uses its own querying functionality to filter these documents based on their contents

Extending Floyd-Hoare Logic for Partial Pre- and Postconditions

Traditional (classical) Floyd-Hoare logic is defined for a case of total pre- and postconditions while programs can be partial. In the chapter we propose to extend this logic for partial conditions. To do this we first construct and investigate special program algebras of partial predicates, functions, and programs. In such algebras program correctness assertions are presented with the help of a special composition called Floyd-Hoare composition. This composition is monotone and continuous. Considering the class of constructed algebras as a semantic base we then define an extended logic – Partial Floyd-Hoare Logic – and investigate its properties. This logic has rather complicated soundness constraints for inference rules, therefore simpler sufficient constraints are proposed. The logic constructed can be used for program verification.

The RISC ProofNavigator: a proving assistant for program verification in the classroom

This paper gives an overview of the RISC ProofNavigator, an interactive proving assistant for the area of program verification. The assistant combines the user-guided top-down decomposition of proofs with the automatic simplification and closing of proof states by an external satisfiability solver. The software exhibits a modern graphical user interface which has been developed with a focus on simplicity in order to make the software suitable for educational scenarios. Nevertheless, some use cases of a certain level of complexity demonstrate that it may be also appropriate for various realistic applications.

On Solving a Problem in Algebraic Geometry by Cluster Computing

We describe a parallel solution to the problem of reliably plotting a plane algebraic curve. The sequential program is implemented in the software library CASA on top of the computer algebra system Maple. The parallel version is based on Distributed Maple, a parallel programming extension written in Java. We evaluate its performance on a cluster of workstations and PCs, on a massively parallel multiprocessor, and on a cluster that couples workstations and multiprocessor.