Alexander Konovalov

Torsion units in integral group rings of Janko simple groups

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel graph of the Janko groups J 1 , J 2 and J 3 is the same as that of the normalized unit group of their respective integral group ring.

Groups St Andrews 2005: Integral group ring of the first Mathieu simple group

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Mathieu group M11. As a consequence, for this group we confirm the conjecture by Kimmerle about prime graphs.

Symbolic Computation Software Composability

We present three examples of the composition of Computer Algebra Systems to illustrate the progress on a composability infrastructure as part of the SCIEnce (Symbolic Computation Infrastructure for Europe) project. One of the major results of the project so far is an OpenMath based protocol called SCSCP (Symbolic Computation Software Composability Protocol). SCSCP enables the various software packages for example to exchange mathematical objects, request calculations, and store and retrieve remote objects, either locally or accross the internet. The three examples show the current state of the GAP, KANT, and MuPAD software packages, and give a demonstration of exposing Macaulay using a newly developed framework.

Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach

OpenDreamKit – “Open Digital Research Environment Toolkit for the Advancement of Mathematics” – is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015–2019, the ecosystem of open-source mathematical software systems. OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Research Environments, customised to meet the varied needs of research projects in pure mathematics and applications.

TORSION UNITS IN INTEGRAL GROUP RINGS OF CONWAY SIMPLE GROUPS

Using the Luthar–Passi method, we investigate the possible orders and partial augmentations of torsion units of the normalized unit group of integral group rings of Conway simple groups Co1, Co2 and Co3.

On service-oriented symbolic computing

Exposing computer algebra systems as computing services allows their further development and integration in complex service-oriented architectures. While existing standards may be used for service deployment and interaction, particularities of services to be built require more specialized solutions. We present recently implemented technical approach aimed to integrate legacy computational algebra software into modern service-oriented and Grid architectures.

Easy composition of symbolic computation software using SCSCP: A new Lingua Franca for symbolic computation

We present the results of the first four years of the European research project SCIEnce-Symbolic Computation Infrastructure in Europe (http://www.symbolic-computing.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 the SCSCP middleware and APIs, outline implementations for various Computer Algebra Systems (CAS), and show how SCSCP-compliant components may be combined to solve scientific problems that cannot be solved within a single CAS, or may be organised into a system for distributed parallel computations. Additionally, we present several domain-specific parallel skeletons that capture commonly used symbolic computations. To ease use and to maximise inter-operability, these skeletons themselves are provided as SCSCP services and take SCSCP services as arguments.

Easy composition of symbolic computation software: a new lingua franca for symbolic computation

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.

Parallelism without Pain: Orchestrating Computational Algebra Components into a High-Performance Parallel System

This paper describes a very high-level approach that aims to orchestrate sequential components written using high-level domain-specific programming into high-performance parallel applications. By achieving this goal, we hope to make parallel programming more accessible to experts in mathematics, engineering and other domains. A key feature of our approach is that parallelism is achieved without any modification to the underlying sequential computational algebra systems, or to the user-level components: rather, all orchestration is performed at an outer level, with sequential components linked through a standard communication protocol, the Symbolic Computing Software Composability Protocol, SCSCP. Despite the generality of our approach, our results show that we are able to achieve very good, and even, in some cases, super-linear, speedups on clusters of commodity workstations: up to a factor of 33.4 on a 28-processor cluster. We are, moreover, able to parallelise a wider variety of problem, and achieve higher performance than typical specialist parallel computational algebra implementations.

Pattern Based Composition of Web Services for Symbolic Computations

The suitability of the BPEL workflow description language for the dynamic composition of Web services representing computational algebra systems is investigated. The prototype implementation of the system for dynamic generation of BPEL workflows and two examples demonstrating the benefits of our approach are described. One of important aspects of the design is that the composition is achieved using standard workflow patterns without any modification of the underlying computational algebra systems, provided they support the OpenMath format.