CALCIUM (Computer Algebra on Cloud Infrastructures) is a pilot project, embedded in the EU Research Infrastructure project VenusC (Virtual MultiDisciplinary Environments Using Cloud Infrastructures) (RI-261565). It focuses on exploiting cloud infrastructures for massively parallel computation, in particular in the domain of computer algebra and symbolic computation.
This page gives an overview of the project. Updates on the progress of CALCIUM are presented on a separate page.
VENUS-C will enable Mathematicians to perform symbolic computations on the cloud far faster than on their own servers, making possible problems that have not previously been computationally viable. Moreover researchers can focus on Mathematical problems without the need to maintain sophisticated parallel symbolic software.
This work builds on the EU-funded SCIEnce (RII3-CT-2005-026133) and the EPSRC-funded HPC-GAP (EP/G 055181) projects. The former supports parallel computational algebra on Grids and has developed several releases of the SymGrid-Par middleware. The latter supports computational algebra on high performance computers. We also expect synergies with the recently started Elvira EPSRC project at St Andrews University.
General purpose computer algebra systems such as Maple or Mathematica simply do not address computation in abstract algebra in any serious way. Maple, for example, can compute with some finite permutation groups, but is far slower than GAP. Only MAGMA and Sage have significant overlap with GAP in core functionality.
Computer algebra systems, like GAP, encode specialised mathematical knowledge in the form of flexibly usable operations. These operations are frequently needed in engineering and scientific activities. However, many of these mathematical operations are very compute-intensive, which limits the usage of these powerful methods. With the availability of massively parallel hardware some ofthese limitations can be eliminated, expanding the application domain of computational algebra.
We build on mature software developed and deployed in the SCIEnce project. GAP has been developed for 16 years by a sizable (109 package authors) international developer base with a quality assurance process. Using a new, domain-specific, skeleton-based approach our SymGrid-Par system has demonstrated excellent speedup on both clusters, and computational Grids. Our experiences show that, in addition to the conventional challenges of high-performance computing such as scalability, algebraic computations pose additional specific problems: they use complex user-defined data structures; exhibit complex recursive structures; make little use of floating-point operations; and exhibit extraordinary (5 orders of magnitude) degrees of dynamic irregularity in both numbers and sizes of tasks.
The primary advance in this field will be in tackling new problem sizes, exploiting parallelism beyond the constraints of shared memory machines.
The primary scientific result is the parallel transformation of non-deterministic finite state automata (FSA) into deterministic FSA. This has many practical applications as FSA are ubiquitous in computer science and is timely as software is inexorably becoming parallel. Far larger FSA can be made deterministic by exploiting Clouds than using current sequential algorithms. We have already contributed in this direction by performing property searches on a range of groups and by implementing a parallel orbit calculation.
A key impact on the scientific community will be that users of computational algebra systems will have readily usable implementations of parametric orbit calculations, and of small group searches in the form of domain-specific parallel patterns. As these computations are representative of classes of problems, the entire class can be solved by instantiating the components of the pattern.
By bringing the SymGrid-Par middleware to Clouds we will provide a software infrastructure tailored to the needs of computational algebra. This will open an entire new application domain to Cloud computing and will attract the interest in a research community that has historically been ill-supported by high-performance computing.
As part of the pilot project we will have access to the MS Azure cloud infrastructure. Additionally, there are cloud infrastructures based on OpenNebula and EMOTIVE, which are provided by project partners.
The CALCIUM project will interact with several currently running projects in the general area of parallel symbolic computation.