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Polyhedral and Algebraic Methods in Computational Geometry provides
a thorough introduction into algorithmic geometry and its
applications. It presents its primary topics from the viewpoints of
discrete, convex and elementary algebraic geometry. The first part
of the book studies classical problems and techniques that refer to
polyhedral structures. The authors include a study on algorithms
for computing convex hulls as well as the construction of Voronoi
diagrams and Delone triangulations. The second part of the book
develops the primary concepts of (non-linear) computational
algebraic geometry. Here, the book looks at Groebner bases and
solving systems of polynomial equations. The theory is illustrated
by applications in computer graphics, curve reconstruction and
robotics. Throughout the book, interconnections between
computational geometry and other disciplines (such as algebraic
geometry, optimization and numerical mathematics) are established.
Polyhedral and Algebraic Methods in Computational Geometry is
directed towards advanced undergraduates in mathematics and
computer science, as well as towards engineering students who are
interested in the applications of computational geometry.
In many fields of modern mathematics specialised scientific
software becomes increasingly important. Hence, tremendous effort
is taken by numerous groups all over the world to develop
appropriate solutions.
This book contains surveys and research papers on mathematical
software and algorithms. The common thread is that the field of
mathematical applications lies on the border between algebra and
geometry. Topics include polyhedral geometry, elimination theory,
algebraic surfaces, Grobner bases, triangulations of point sets and
the mutual relationship. This diversity is accompanied by the
abundance of available software systems which often handle only
special mathematical aspects. Therefore the volume's other focus is
on solutions towards the integration of mathematical software
systems. This includes low-level and XML based high-level
communication channels as well as general framework for modular
systems."
A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.
The goal of this book is to explain, at the graduate student level,
connections between tropical geometry and optimization. Building
bridges between these two subject areas is fruitful in two ways.
Through tropical geometry optimization algorithms become applicable
to questions in algebraic geometry. Conversely, looking at topics
in optimization through the tropical geometry lens adds an
additional layer of structure. The author covers contemporary
research topics that are relevant for applications such as
phylogenetics, neural networks, combinatorial auctions, game
theory, and computational complexity. This self-contained book grew
out of several courses given at Technische Universitat Berlin and
elsewhere, and the main prerequisite for the reader is a basic
knowledge in polytope theory. It contains a good number of
exercises, many examples, beautiful figures, as well as explicit
tools for computations using $\texttt{polymake}$.
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Mathematical Software - ICMS 2020 - 7th International Conference, Braunschweig, Germany, July 13-16, 2020, Proceedings (Paperback, 1st ed. 2020)
Anna Maria Bigatti, Jacques Carette, James H. Davenport, Michael Joswig, Timo de Wolff
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R1,628
Discovery Miles 16 280
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Ships in 10 - 15 working days
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This book constitutes the proceedings of the 7th International
Conference on Mathematical Software, ICMS 2020, held in
Braunschweig, Germany, in July 2020. The 48 papers included in this
volume were carefully reviewed and selected from 58 submissions.
The program of the 2020 meeting consisted of 20 topical sessions,
each of which providing an overview of the challenges, achievements
and progress in a environment of mathematical software research,
development and use.
In dem Lehrbuch wird eine mathematisch orientierte Einfuhrung in
die algorithmische Geometrie gegeben. Im ersten Teil werden
"klassische" Probleme und Techniken behandelt, die sich auf
polyedrische (= linear begrenzte) Objekte beziehen. Hierzu gehoeren
beispielsweise Algorithmen zur Berechnung konvexer Hullen und die
Konstruktion von Voronoi-Diagrammen. Im zweiten Teil werden
grundlegende Methoden der algorithmischen algebraischen Geometrie
entwickelt und anhand von Anwendungen aus Computergrafik,
Kurvenrekonstruktion und Robotik illustriert. Das Buch eignet sich
fur ein fortgeschrittenes Modul in den derzeit neu konzipierten
Bachelor-Studiengangen in Mathematik und Informatik.
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