Abelian functions associated with genus three algebraic curves

We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and an advancement of efficient symbolic computation techniques has allowed for recent progress in this area. In this paper we focus on the genus three cases, comparing the two canonical classes of hyperelliptic and trigonal curves. We present new addition formulae, derive bases for the spaces of Abelian functions and discuss the differential equations such functions satisfy.Comment: 34 page

An implementation of CAD in Maple utilising problem formulation, equational constraints and truth-table invariance

Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications within algebraic geometry and beyond. We recently reported on a new implementation of CAD in Maple which implemented the original algorithm of Collins and the subsequent improvement to projection by McCallum. Our implementation was in contrast to Maple's in-built CAD command, based on a quite separate theory. Although initially developed as an investigative tool to compare the algorithms, we found and reported that our code offered functionality not currently available in any other existing implementations. One particularly important piece of functionality is the ability to produce order-invariant CADs. This has allowed us to extend the implementation to produce CADs invariant with respect to either equational constraints (ECCADs) or the truth-tables of sequences of formulae (TTICADs). This new functionality is contained in the second release of our code, along with commands to consider problem formulation which can be a major factor in the tractability of a CAD. In the report we describe the new functionality and some theoretical discoveries it prompted. We describe how the CADs produced using equational constraints are able to take advantage of not just improved projection but also improvements in the lifting phase. We also present an extension to the original TTICAD algorithm which increases both the applicability of TTICAD and its relative benefit over other algorithms. The code and an introductory Maple worksheet / pdf demonstrating the full functionality of the package are freely available online.Comment: 12 pages; University of Bath, Dept. Computer Science Technical Report Series, 2013-02, 201

The road less travelled: leadership and engagement of learners in a collaborative learning environment

[Abstract]: Historically at USQ we have taught information literacy classes in a very traditional instructional format. The training labs have rows of seating facing forward, and large computer monitors in front of participants. The trainer stands at the front with a whiteboard and projection screen. With innovations in teaching styles and developments in learning spaces, we are this year initiating a change to information literacy classes. Traditional training labs and teaching styles have been replaced by collaborative group learning spaces and a guided teaching style. As part of a refurbishment project, one of our training labs and an office area of the library have been set up to support collaborative learning. Subsequently in Semester 1, 2009 we will begin using the new collaborative learning facilities for all generic information literacy classes, and some faculty classes. In the past our training has focussed on the transmission of information and we have not fully engaged our students in the learning process. We have used PowerPoint’s and the Library website to conduct classes. Whilst the basic information we want to impart to students will be the same, the way we do this and hopefully the learning outcomes will change significantly with the shift to a collaborative teaching style and environment

Higher Genus Abelian Functions Associated with Cyclic Trigonal Curves

We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain areas of the theory. We present solutions to the Jacobi inversion problem, sets of relations between the Abelian function, links to the Boussinesq equation and a new addition formula

On the Front Lines of Public Policy

UM Law students get in the thick of tobacco policy, international terrorism regulations, drug treatment, even the mundane yet complex rules of homeowners\u27 associations. The lives they change, now and in the jobs they secure, reach well beyond their own

Formulating problems for real algebraic geometry

We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both performance and output and summarise what may be done to assist with this choice. We then survey other questions of problem formulation and algorithm optimisation that have become pertinent following advances in CAD theory, including both work that is already published and work that is currently underway. With implementations now in reach of real world applications and new theory meaning algorithms are far more sensitive to the input, our thesis is that intelligently formulating problems for algorithms, and indeed choosing the correct algorithm variant for a problem, is key to improving the practical use of both quantifier elimination and symbolic real algebraic geometry in general.Comment: To be presented at The "Encuentros de \'Algebra Computacional y Aplicaciones, EACA 2014" (Meetings on Computer Algebra and Applications) in Barcelon

A Call for Change: The Evolution of the Modern Documentary from Informative Media to Persuasive Platform

In the past several years, new documentaries have begun to evolve from informative media to persuasive platform as a result of changing cultural contexts and ideologies. These four films – Sicko, Food Inc., Waiting for Superman, and Inside Job effectively utilize common narratives and themes to present audiences with calls for reform in critical areas such as food safety, quality education, access to healthcare, and financial regulation. This shift reflects a transformation of the valuation of knowledge and how it serves various conflicting group interests

Setting a Benchmark for Baltimore\u27s Courts

The Hon. Ellen Moses Heller \u2777--Setting a Benchmark for Baltimore\u27s Court

All Wired Up and Ready to Go

The School of Law\u27s new facility is one of the most technologically advanced legal education buildings in the country. Read what the buzz is all about