Paul Zimmermann – författare

Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors.

SageMath, or Sage for short, is an open-source mathematical software system based on the Python language and developed by an international community comprising hundreds of teachers and researchers, whose aim is to provide an alternative to the commercial products Magma, Maple, Mathematica, and MATLAB®. To achieve this, Sage relies on many open-source programs, including GAP, Maxima, PARI, and various scientific libraries for Python, to which thousands of new functions have been added. Sage is freely available and is supported by all modern operating systems.Sage provides a wonderful scientific and graphical calculator for high school students, and it efficiently supports undergraduates in their computations in analysis, linear algebra, calculus, etc. For graduate students, researchers, and engineers in various mathematical specialties, Sage provides the most recent algorithms and tools, which is why several universities around the world already use Sage at the undergraduate level. Computational Mathematics with SageMath, written by researchers and by teachers at the high school, undergraduate, and graduate levels, focuses on the underlying mathematics necessary to use Sage efficiently and is illustrated with concrete examples. Part I is accessible to high school and undergraduate students and Parts II, III, and IV are suitable for graduate students, teachers, and researchers.This book is available under a Creative Commons license at sagebook.gforge.inria.fr.

​Die Entscheidung zur Funktionsverlagerung im internationalenKonzern wird durch die Preisgrenzen der beteiligten Unternehmen imFremdvergleich und die betriebswirtschaftliche Preisgrenze aus Konzernsicht bestimmt. Deshalb wirken die einzelnen wirtschaftlichen und steuerlichen Einflussfaktoren unterschiedlich auf die Verlagerung, je nachdem, welche Preisgrenze sie beeinflussen.Anhand einer Analyse dieser Faktoren lassen sich die Stärken und Schwächen der deutschen Regelung zur steuerlichen Behandlung von Funktionsverlagerungen angesichts des Leitbildes einer möglichst entscheidungsneutralen Besteuerung ermitteln. Dies führt zu einer differenzierten Kritik der bestehenden steuerlichen Behandlung von Funktionsverlagerungen, die zwischen wirtschaftlich begründeten Barrieren und (unerwünschten) steuerlichen Hindernissen unterscheidet.Vor dem Hintergrund einer optimalen Ressourcenallokation im Konzern sind gerade die letzteren Anknüpfungspunkt für Korrekturen und Verbesserungsvorschläge.