Tropical algebraic geometry in Maple: A preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients

AbstractFinding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic–numeric computing. Taking a tropical view of this problem leads to efficient preprocessing techniques, applying polyhedral methods to the exact exponents and numerical techniques to the approximate coefficients. With Maple we will illustrate our use of tropical algebraic geometry

Macsyma: A personal history

AbstractThe Macsyma system arose out of research on mathematical software in the AI group at MIT in the 1960s. Algorithm development in symbolic integration and simplification arose out of the interest of people, such as the author, who were also mathematics students. The later development of algorithms for the GCD of sparse polynomials, for example, arose out of the needs of our user community. During various times in the 1970s the computer on which Macsyma ran was one of the most popular nodes on the ARPANET. We discuss the attempts in the late 70s and the 80s to develop Macsyma systems that ran on popular computer architectures. Finally, we discuss the impact of the fundamental ideas in Macsyma on the author’s current research on large scale engineering and socio-technical systems

A Polyhedral Method to Compute All Affine Solution Sets of Sparse Polynomial Systems

To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible decomposition of a variety is typically understood in affine space, including also those components with zero coordinates. We present a polyhedral method to compute all affine solution sets of a polynomial system. The method enumerates all factors contributing to a generalized permanent. Toric solution sets are recovered as a special case of this enumeration. For sparse systems as adjacent 2-by-2 minors our methods scale much better than the techniques from numerical algebraic geometry

Formula Simplification for Real Quantifier Elimination Using Geometric Invariance (Computer Algebra --Theory and its Applications)

Formulating a simple and adequate quantified first-order formula is crucial for applying real quantifier elimination (QE) efficiently. In general, generating simple formulas or simplifying formulas for efficient QE involves human interaction. In this paper, we present simplification algorithms for quantified first-order formulas over the real numbers to speed up QE. We present experimental results for more than 10, 000 benchmark problems to examine the effectiveness of our simplification algorithms

Redefining military memorials and commemoration and how they have changed since the 19th century with a focus on Anglo-American practice

This thesis is a study of military memorials and commemoration with a focus on Anglo-American practice. The main question is: How has history defined military memorials and commemoration and how have they changed since the 19th century. In an effort to resolve this, the work examines both historic and contemporary forms of memorials and commemoration and establishes that remembrance in sites of collective memory has been influenced by politics, conflicts and religion. Much has been written since the Great War about remembrance and memorialization; however, there is no common lexicon throughout the literature. In order to better explain and understand this complex subject, the work includes an up-to-date literature review and for the first time, terminologies are properly explained and defined. Particular attention is placed on recognizing important military legacies, being familiar with spiritual influences and identifying classic and new signs of remembrance. The thesis contends that commemoration is composed of three key principles – recognition, respect and reflection – that are intractably linked to the fabric of memorials. It also argues that it is time for the study of memorials to come of age and proposes Memorialogy as an interdisciplinary field of study of memorials and associated commemorative practices. Moreover, a more modern, adaptive, General Classification System is presented as a means of identifying and re-defining memorials according to certain groups, types and forms. Lastly, this thesis examines how peacekeeping and peace support operations are being memorialized and how the American tragic events of 11 September 2001 and the war in Afghanistan have forever changed the nature of memorials and commemoration within Canada and elsewhere. This work goes beyond what has been studied and written about over the last century and provides a deeper level of analysis and a fresh approach to understanding the field of Memorialogy

Beanstalk to macca tree : the development of the national pantomine by the little theatre movement of Jamaica, 1941-2003

Greta Bourke and Henry Fowler, co-founders of the Little Theatre Movement of Jamaica, initiated the L TM Pantomime tradition in 1941 to raise funds for an experimental theatre, which would both house contemporary trends from Europe and America and carve out a creative space for the indigenous culture of an emergent New Jamaica.The LTM actively developed the Pantomime audience at the Ward Theatre to reflect a cross-section of society. Coachloads of adults and children from country districts joined the established middle-class theatregoers as well as representatives of the inner city 'people of the yard'. Gradually, the original English-pantomime style production metamorphosed into a different entity. Topical reference, proverbial wisdom, song, dance and vibrant colour were mixed and expressed in language, which zigzagged along the continuum between Jamaican Standard English and Patwa.Over six decades, Jamaican Pantomime has created a prestigious performative space for the retelling of many episodes from the life story of an old island. Intrinsic to this context is a system of shared beliefs which operates on a number of levels: the value of received wisdom, the redemptive nature of Christian faith, Anancyism as a strategy of survival, and national aspirations for unity based on the principle of mutual respect.The Little Theatre complex, which opened in 1961, housed the national schools of drama and dance before they became part of an integrated Visual and Performing Arts College for the island. Furthermore, a catalogue of the thousands of people who have been involved in LTM productions over six decades reads as a Who's Who of Jamaican cultural development in the twentieth century.Instead of merely mimicking the English model. the L TM Pantomime evolved into a distinct form of indigenous theatre and rekindled the folk tradition as an expression of national identity within the context of contemporary popular culture

The Scottish orchestras and new music, 1945-2015

This dissertation critically examines the presentation of new music in live concerts by three Scottish orchestras. It considers what they have commissioned, what performed, the context in which the music has been programmed, and who was involved. The orchestras are the three which are established on a permanent basis and give regular subscription series in Scotland: the BBC Scottish Symphony, Royal Scottish National, and Scottish Chamber Orchestras. The study contributes to the debate around classical music programming of new music, taking these orchestras as examples. It asks how in practice some of those responsible for programming in the period from 1945 to 2015 have reconciled conflicting expectations and desires. On the one hand there is a vast heritage, an 'imaginary museum', of old music, and it is this which most audiences want to hear. On the other hand, living composers continue to write and some audiences want to hear their music performed. This is music which speaks of and to our own times. The dissertation asks about some of the factors which have influenced programmers' decisions and how those programmers have presented new music to the public — alongside the old, in special events, or in another way. It considers the advantages and disadvantages of each type of programming. Underlying these questions is the changing status in the west of western classical music. Even if it is not dying, as some commentators have stated, it is but one among many musics, with a relatively small market share. Given that situation, are orchestras, which are heavily dependent on public and/or private funding, still relevant to contemporary society? And if so, is part of their role to reflect aspects of that society by playing new music

The Rifle Brigade 1800 to c.1870 : a study of social, cultural and religious attitudes.

This dissertation analyses the social, cultural and religious outlook of the officers and men of the Rifle Brigade, a regiment of the British army, between 1800 and about 1870, and examines the relationship between that corps and British civilian society. Chapter 1 outlines the structure and military record of the regiment, describes its links into the wider army, and examines the military and non-military careers of Riflemen, and their social backgrounds. Chapter 2 presents evidence for reforming and conservative professional attitudes, and argues for the importance to them of an ideal of regenerated gentlemanliness. Chapter 3 describes the operation of patronage and the links it created with civilian society, and it analyses the views of merit that und~rpinned the system. Chapter 4 brings together evidence for the reading of officers and men, and the theatre they saw and performed themselves. It shows how these acted as a channel for a range of information, ideas and attitudes to enter the regiment from civilian society, and so fostered a shared outlook. Chapters 5 and 6 look at the extent and nature of religious belief among Riflemen, taking into account their backgrounds and subsequent careers, and argue both that Christianity coloured attitudes to a range of conduct, and that Riflemen adhered to forms of institutional and cultural religion that should be set beside personal piety. The conclusion highlights the role of the ideal of gentlemanliness in guiding officers and in shaping a culture shared across ranks and across the civilian-military divide. Two appendices are provided. The first describes the method used for the analysis of officers' careers, and the second is a genealogical table showing their interrelation