CHAMP: A Cherednik Algebra Magma Package

We present a computer algebra package based on Magma for performing computations in rational Cherednik algebras at arbitrary parameters and in Verma modules for restricted rational Cherednik algebras. Part of this package is a new general Las Vegas algorithm for computing the head and the constituents of a module with simple head in characteristic zero which we develop here theoretically. This algorithm is very successful when applied to Verma modules for restricted rational Cherednik algebras and it allows us to answer several questions posed by Gordon in some specific cases. We could determine the decomposition matrices of the Verma modules, the graded G-module structure of the simple modules, and the Calogero-Moser families of the generic restricted rational Cherednik algebra for around half of the exceptional complex reflection groups. In this way we could also confirm Martino's conjecture for several exceptional complex reflection groups.Comment: Final version to appear in LMS J. Comput. Math. 41 pages, 3 ancillary files. CHAMP is available at http://thielul.github.io/CHAMP/. All results are listed explicitly in the ancillary PDF document (currently 935 pages). Please check the website for further update

A Pattern-based Foundation for Language-Driven Software Engineering

This work brings together two fundamental ideas for modelling, programming and analysing software systems. The first idea is of a methodological nature: engineering software by systematically creating and relating languages. The second idea is of a technical nature: using patterns as a practical foundation for computing. The goal is to show that the systematic creation and layering of languages can be reduced to the elementary operations of pattern matching and instantiation and that this pattern-based approach provides a formal and practical foundation for language-driven modelling, programming and analysis. The underpinning of the work is a novel formalism for recognising, deconstructing, creating, searching, transforming and generally manipulating data structures. The formalism is based on typed sequences, a generic structure for representing trees. It defines basic pattern expressions for matching and instantiating atomic values and variables. Horizontal, vertical, diagonal and hierarchical operators are different ways of combining patterns. Transformations combine matching and instantiating patterns and they are patterns themselves. A quasiquotation mechanism allows arbitrary levels of meta-pattern functionality and forms the basis of pattern abstraction. Path polymorphic operators are used to specify fine-grained search of structures. A range of core concepts such as layering, parsing and pattern-based computing can naturally be defined through pattern expressions. Three language-driven tools that utilise the pattern formalism showcase the applicability of the pattern-approach. Concat is a self-sustaining (meta-)programming system in which all computations are expressed by matching and instantiation. This includes parsing, executing and optimising programs. By applying its language engineering tools to its own meta-language, Concat can extend itself from within. XMF (XML Modeling Framework) is a browser-based modelling- and meta-modelling framework that provides flexible means to create and relate modelling languages and to query and validate models. The pattern functionality that makes this possible is partly exposed as a schema language and partly as a JavaScript library. CFR (Channel Filter Rule Language) implements a language-driven approach for layered analysis of communication in complex networked systems. The communication on each layer is visible in the language of an “abstract protocol” that is defined by communication patterns

A pattern-based foundation for language-driven software engineering

This work brings together two fundamental ideas for modelling, programming and analysing software systems. The first idea is of a methodological nature: engineering software by systematically creating and relating languages. The second idea is of a technical nature: using patterns as a practical foundation for computing. The goal is to show that the systematic creation and layering of languages can be reduced to the elementary operations of pattern matching and instantiation and that this pattern-based approach provides a formal and practical foundation for language-driven modelling, programming and analysis. The underpinning of the work is a novel formalism for recognising, deconstructing, creating, searching, transforming and generally manipulating data structures. The formalism is based on typed sequences, a generic structure for representing trees. It defines basic pattern expressions for matching and instantiating atomic values and variables. Horizontal, vertical, diagonal and hierarchical operators are different ways of combining patterns. Transformations combine matching and instantiating patterns and they are patterns themselves. A quasiquotation mechanism allows arbitrary levels of meta-pattern functionality and forms the basis of pattern abstraction. Path polymorphic operators are used to specify fine-grained search of structures. A range of core concepts such as layering, parsing and pattern-based computing can naturally be defined through pattern expressions. Three language-driven tools that utilise the pattern formalism showcase the applicability of the pattern-approach. Concat is a self-sustaining (meta-)programming system in which all computations are expressed by matching and instantiation. This includes parsing, executing and optimising programs. By applying its language engineering tools to its own meta-language, Concat can extend itself from within. XMF (XML Modeling Framework) is a browser-based modelling- and meta-modelling framework that provides flexible means to create and relate modelling languages and to query and validate models. The pattern functionality that makes this possible is partly exposed as a schema language and partly as a JavaScript library. CFR (Channel Filter Rule Language) implements a language-driven approach for layered analysis of communication in complex networked systems. The communication on each layer is visible in the language of an “abstract protocol” that is defined by communication patterns.EThOS - Electronic Theses Online ServiceGBUnited Kingdo