Wolfram Decker – författare

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.

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.