Abstract. This paper demonstrates that it is possible to obtain good, scalable parallel performance by coordinating multiple instances of unaltered sequential computational algebra systems in order to deliver a single parallel system. The paper presents the first substantial parallel performance results for SymGrid-Par, a system that orchestrates computational algebra components into a high-performance parallel application. We show that SymGrid-Par is capable of exploiting different parallel/multicore architectures without any change to the computational algebra component. Ultimately, our intention is to extend our system so that it is capable of orchestrating heterogeneous computations across a high-performance computational Grid. For now, we illustrate our approach with a single, unmodified production computational algebra system, GAP, running on two common commodity architectures — a homogeneous cluster and an eight-core system. Computational algebra applications are large, specialised, and symbolic, rather than the more commonly studied numerical applications. They also exhibit high levels of irregularity, and multiple levels of irregularity. We demonstrate that for three small but representative algebraic computations, good parallel speedup is possible relative to a sequential GAP system running on a single processor/core. We compare the performance of the orchestrated system with that of parGAP, an established parallel implementation of GAP, demonstrating

Declarative programming languages can play an important role in the process of designing and implementing parallel systems. They bridge the gap between a high-level specification, with proven properties of the overall system, and the execution of the system on real hardware. Efficiently exploiting parallelism on a wide range of architectures is a challenging task and should in our view be handled by a sophisticated runtime environment. Based on this design philosophy we have developed and formalised Glasgow parallel Haskell (GpH), and implemented it as a conservative extension of the Glasgow Haskell Compiler. The high-level nature of declarative languages eases the task of mapping an algebraic specification down to executable code. In fact, the operational components of the specification can already be considered an implementation, with the associated properties acting as assertions in the program. Based on a formal model of the declarative language, the validity of these properties can be established by manual proof, which works on a level of detail similar to the specification language itself. Many operational aspects, usually complicating

We present the results of the first four years of the European research project SCIEnce (www.symbolic-computation.org), which aims to provide key infrastructure for symbolic computation research. A primary outcome of the project is that we have developed a new way of combining computer algebra systems using the Symbolic Computation Software Composability Protocol (SCSCP), in which both protocol messages and data are encoded in the OpenMath format. We describe SCSCP middleware and APIs, outline some implementations for various Computer Algebra Systems (CAS), and show how SCSCP-compliant components may be combined to solve scientific problems that can not be solved within a single CAS, or may be organised into a system for distributed parallel computations.