Michael Joswig – författare

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 Gröbner 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.

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.

This book presents version 1.0 of the new Computer Algebra System OSCAR.

Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:

ANTIC for number theory, GAP for group and representation theory,  polymake for polyhedral and tropical geometry, and  Singular for commutative algebra and algebraic geometry.

It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.

It is freely available, open source software.

The book is an invitation to use OSCAR.  With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets.  These are valuable for interested researchers from graduate students through established experts.