Wolfram Decker

Claus Fieker

Michael Joswig

Christian Eder

Max Horn

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.

Algorithms and Examples

The Computer Algebra System OSCAR

Christoph Lossen

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

A Quick Start using SINGULAR

Computing in Algebraic Geometry

Gerhard Pfister

A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments.

A First Course in Computational Algebraic Geometry

Gebhard Böckle

Gunter Malle

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Mathias Schulze

This book arose from a conference on “Singularities and Computer Algebra” which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel’s 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra.Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Schönemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists.The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.

Wolfram Decker

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