Our short research visits programme successfully continues. Since the beginning of the project, we have received 14 applications for travel support, and 12 visits already took place. This is an overview of summer travel activities which were fully or partially funded by CoDiMa after the publication of the previous travel update.
In June, Dmitrii Pasechnik (Oxford) attended the Dagstuhl Seminar “Complexity of Symbolic and Numerical Problems“, dedicated to Dmitry Grigoriev’s (a distinguished complexity theorist from CNRS (France), and Dmitrii’s long-term collaborator) 60th jubilee. Dmitrii gave a talk on a computational symbolic-numeric topic related to computational geometry, where in particular a prototype implementation of one of the main procedure was implemented in Sagemath system (see http://arxiv.org/abs/1409.3130). He also held informal discussions and conducted research with Ilya Ponomarenko, a leading researcher in graphs isomorphism problem and permutation groups. Using GAP and another software package, COCO, they were able to solve an open problem from the joint paper by Ilya Ponomarenko and Mikhail Muzychuk. Questions related to a possible integration of COCO into GAP were discussed as well.
Later, Dmitrii Pasechnik was visited for several days by Nathann Cohen (Orsay, France), who is one of lead developers of Sagemath, in particular of its combinatorics and optimisation parts. They worked together on a number of important technical issues in Sagemath and its interfaces to GAP and other software packages. A considerable progress has been achieved on a variety of topics: more than 10 Sagemath tickets were reviewed, and around 10 new tickets were opened, including those related to GAP-SageMath integration.
Jim Howie (Heriot-Watt) visited Olexandr Konovalov in St Andrews for a day in July to discuss an ongoing joint work related to a conjecture of Gerhard Rosenberger on generalised triangle groups and optimise GAP code used for computational experiments in this project.
In July, the University of Bath became a place for the two central events for the symbolic and algebraic computation community – The 40th International Symposium on Symbolic and Algebraic Computation (ISSAC 2015) and the 7th International Workshop on Parallel Symbolic Computation (PASCO 2015). There was a number of great plenary talks given, a number of new and ongoing exciting software packages presented, and also a great opportunity to meet other members of the community. CoDiMa supported participation of Dmitrii Pasechnik in ISSAC and of Hans-Wolfgang Loidl (Heriot-Watt) in PASCO. Plenty of informal discussions took place on topics of importance for GAP and Sagemath projects, both of techical and general nature, together with Steve Linton, Olexandr Konovalov and Alexander Hulpke. In particular we discussed and made plans on how to revive vector enumeration software, formerly included in GAP, but then abandoned around GAP release 4.2. A long discussion on better integration of FriCAS, a fork of Axiom CAS, into Sagemath, also took place with its lead developer Waldek Hebisch. Further details on PASCO are given in Hans-Wolfgang’s travel report: PASCO is a series of international workshops on Parallel Symbolic Computation and is a unique venue of combining foundational computer algebra research with complex system building and the associated research challenges of high-performance computing in a domain featuring irregular and highly dynamic parallelism. The series started with workshops on Computer Algebra and Parallelism (CAP), in Grenoble in 1988, and the first instance of PASCO was organised by RISC Linz in 1994. PASCO’15 featured 13 presentations in total, and 3 invited talks by Allan Steel on “Exploiting Tesla GPUs with Magma”, by Jean-Louis Roche on “Interactive Computations and Outsourcing”, and by Julien Langou on “Overview of Recent Algorithms, Trends and Libraries in Numerical Dense Linear Algebra”. The PASCO series has proven to be a very fertile ground for new ideas in the challenging domain of parallel algorithms, systems and languages for symbolic computation. It is planned to make the instances in this series more regular, aiming for a workshop every two years.”
Alexandre Borovik and Sukru Yancinkaya had a very fruitful “research in pairs”-like visit to Nesin Mathematics Village (Turkey) and during three weeks there they have made further breakthroughs in their work on a new class of probabilistic “black box” algorithms for computational group theory, which may eventually become implemented in our software.
Derek Holt (University of Warwick) visited St Andrews for several days in August. One of the topics that was discussed during this visit was extending the library of transitive groups. The transitive groups of degrees up to 47 have been enumerated, and degree 48 is the next challenge. There are likely to be considerably more such groups than for all smaller degrees. Primitive groups of degree 48, and imprimitive groups with minimal blocksize at least 4 could be easily found, but those with blocksizes 2 and 3 will be much more difficult. We plan first to attempt to enumerate the groups with blocksize 2 and use SCSCP package to check 25000 different cases of groups with blocksize 2 in parallel.
Rebecca Waldecker (Martin-Luther-Universität Halle-Wittenberg) visited St Andrews for a week in August for collaborative work on algorithms for permutation groups and their GAP implementations. She also gave a talk “Fixity and subgroup structure” at the CIRCA Algebra Seminar.
Further details about the CoDiMa short research visits programme and instructions how to apply are available here.