This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
Lonely Planet's France is your passport to the most relevant, up-to-date advice on what to see and skip, and what hidden discoveries await you. Explore Bordeaux's wineries, lose yourself in Paris, or reach new heights in the French Alps; all with your trusted travel companion. Get to the heart of France and begin your journey now! Inside Lonely Planet's France Travel Guide: Up-to-date information - all businesses were rechecked before publication to ensure they are still open after 2020s COVID-19 outbreak NEW pull-out, passport-size 'Just Landed' card with wi-fi, ATM and transport info - all you need for a smooth journey from airport to hotel Improved planning tools for family travellers - where to go, how to save money, plus fun stuff just for kids What's New feature taps into cultural trends and helps you find fresh ideas and cool new areas our writers have uncovered Colour maps and images throughout Highlights and itineraries help you tailor your trip to your personal needs and interests Insider tips to save time and money and get around like a local, avoiding crowds and trouble spots Essential info at your fingertips - hours of operation, phone numbers, websites, transit tips, prices Honest reviews for all budgets - eating, sleeping, sightseeing, going out, shopping, hidden gems that most guidebooks miss Cultural insights give you a richer, more rewarding travel experience - history, people, music, landscapes, wildlife, cuisine, politics Over 55 maps Covers Brittany, Normandy, Lille, Flanders & the Somme, Paris, Ile de France, Champagne, Alsace & Lorraine, Bordeaux, Nantes & the Atlantic Coast, French Basque Country, the Pyrenees, Toulouse, Dordogne, Limousin & the Lot, Auvergne, Burgundy, French Alps, Jura Mountains, Lyon, Rhone Valley, Languedoc-Roussillon, Provence, Monaco, Cote d'Azur, Corsica The Perfect Choice: Lonely Planet's France, our most comprehensive guide to France, is perfect for both exploring top sights and taking roads less travelled. Looking for just the highlights? Check out Best of France, a handy-sized guide focused on the can't-miss sights. For a quick trip to Paris, check out Pocket Paris, a handy-sized guide focused on the can't-miss sights for a quick trip. About Lonely Planet: Lonely Planet is a leading travel media company, providing both inspiring and trustworthy information for every kind of traveller since 1973. Over the past four decades, we've printed over 145 million guidebooks and phrasebooks for 120 languages, and grown a dedicated, passionate global community of travellers. You'll also find our content online, and in mobile apps, videos, 14 languages, armchair and lifestyle books, ebooks, and more, enabling you to explore every day. 'Lonely Planet guides are, quite simply, like no other.' New York Times 'Lonely Planet. It's on everyone's bookshelves; it's in every traveller's hands. It's on mobile phones. It's on the Internet. It's everywhere, and it's telling entire generations of people how to travel the world.' Fairfax Media (Australia)
This book examines the FinTech revolution from a data privacy perspective. It analyzes key players on the FinTech market and the developments in various market segments. Particular attention is paid to an empirical analysis of the privacy statements of 505 German FinTech firms and how they were adapted after the General Data Protection Regulation (GDPR) entered into effect in May 2018. The analysis also includes 38 expert interviews with relevant stakeholders from supervisory and regulatory authorities, the financial and FinTech industry, leading consulting firms and consumer protection agencies. By adopting this approach, the book identifies key regulatory needs, offers a valuable asset for practitioners and academics alike, and shares intriguing insights for lawyers, economists and everyone interested in FinTech and data privacy.
Erased de Kooning Drawing ist ein Kunstwerk, das auf radikale Weise die Definition von Kunst und das Verständnis von Autorschaft herausfordert. Drei amerikanische Künstler waren 1953 an seiner Erschaffung beteiligt: Robert Rauschenberg radierte eine Zeichnung Willem de Koonings aus, der mit einem gewissen Widerwillen sein Einverständnis gegeben hatte. Jasper Johns versah es anlässlich seiner ersten Präsentation mit einem Label, das maßgeblich zu seiner Wahrnehmung als eigenständigem Werk beitrug. Das zu etwas Neuem transformierte Blatt wurde in den 1950er-Jahren als Neo-Dada aufgefasst, in den 1960ern als Beginn der Konzeptkunst und in den 1980er-Jahren als Aufbruch in die Postmoderne. Zahlreiche Künstler*innen bezogen sich auf das Werk und Rauschenberg selbst griff es immer wieder auf. Es erwies sich als Testfall für Bestimmungen von Modernismus, Literalismus und Postmodernismus. Gregor Stemmrichs kenntnisreiche kunsttheoretische Betrachtung arbeitet die anhaltende Relevanz des Werks für die Theorie des Bildes, des Index, der Spur, des Allegorischen und der Frage nach Appropriation heraus.
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.
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