We report on a project on parallelizing parts of the software library CASA for computing with and reasoning about objects in algebraic geometry with applications in computer aided geometric design and solid modeling. CASA is implemented in the language of the computer algebra system Maple; we therefore have developed \Distributed Maple" as an environment for executing parallel Maple programs on multiple computers of a network. Using this environment, we have started the parallelization of some important CASA algorithms; for a particular subproblem we achieve a speedup of 15 on a heterogeneous network with 24 processors distributed among PCs, workstations, and shared memory multiprocessors. 1 Introduction This paper describes an ongoing eort on developing a distributed system for solving problems in algebraic geometry with applications in computer aided geometric design and solid modeling. The starting point of our work is the software library CASA (computer algebra software for cons...

We describe how a para-functional programming language is applied to implementing parallel computer algebra algorithms on a shared memory multiprocessor. The language we use is pD, a small functional language that we have 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 program into parallel C code with explicit task creation and synchronization constructs. The implemented para-functional programs perform as efficient as manually coded parallel C programs. 1 Introduction While most computer algebra algorithms [3] are based on the concept of pure functions, real-world computer algebra programs are for performance reasons usually written in a low-level imperative style (typically in C). Consequently, there is little resemblance between the notation in which the mathematical theory is formulated a...

This paper sketches an environment for distributed education that supports the lecturer in preparing and performing a computer-supported session over the network ("virtual classroom"). This task is particularly challenging because it requires the coordination of concurrent activities operating in real-time on objects of different types located in a distributed network environment. We describe the CONCERT software architecture that can be implemented with realistic efforts in the mid-term future and allows non-expert users to perform such a task. Since technology is rapidly evolving, we focus on the design of an abstract architecture under which various technologies can be integrated and on top of which different programming interfaces can be built. This architecture can be implemented in form of an application framework i.e. of an object-oriented software library into which application/system-specific components can be plugged. Our investigation is accompanied by a detail...

of some characteristics of softwares for parallel computer algebra. SBSH means Sugarbush. PCLBSTM means PACLIB/STURM and PCGVR PAC/GIVARO. Conclusions. Major problems that appears in the design and implementation of parallel computer algebra systems (on-line scheduling of tasks, distributed garbage collection) are studied in the more general context of modern parallel programming languages. Also, parallel computer algebra focus nowdays on two directions. First, a development effort has to be done to integrate a modern parallel language in a general purpose computer algebra system with its huge libraries of complex algorithms. Second, active research should be done in the design of efficient and portable parallel algorithms for more complex problems. Thierry Gautier (INRIA, LMC-IMAG), Hoon Hong (NCSU), Jean-Louis Roch (LMC-IMAG), Gilles Villard (CNRS, LMC-IMAG), Wolfgang Schreiner (RISCLinz) References ...

measures used to analyze algorithms are depth and work; arithmetic and communication costs are distinguished. The one corresponds to operations performed (macro-instructions nodes) while the other to access in the shared memory (data dependencies nodes). Arithmetic work and depth have been used for many years to analyze performances of parallel algorithms 8 In such a DFG, any output may be equivalently seen as a polynomial whose indeterminates are the inputs. The arithmetic degree is then the maximal degree of polynomials corresponding to the outputs. 28 CHAPTER 1. PARALLEL EFFICIENT ALGORITHMS [9, 55, 35, 28, 6]. Due to experimental constraints, the relevance of communications costs (i.e. total communication traffic -- work - and total communications delay) has been pointed out to obtain practical performant programs [5, 19]. Since minimizing communications overhead and minimizing parallel time are antagonist, good trade-offs have been studied for several common algorithms [47, 1...

A functor is a parameterized program module i.e. a function that takes modules as arguments and returns a module as its result. A higher-order functor deals in the same way with modules whose components are functors themselves. We propose to develop a generic compilation system for the construction of high-performance mathematical software libraries for scientific and technical application domains. This system has the following features: 1. It is based on a powerful higher-order functor language. 2. It is an open library that can be retargeted to any core language. 3. It is able to resolve functor instantiation at compile-time. The functor language is expressive enough to build all types and type constructors without referring to the core language (thus maximizing flexibility) and to express all interactions between modules by parameterization (thus maximizing reusability). By compile-time instantiation, genericity does not cause any execution overhead; by automatically sharing instant...