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.

Gebhard Böckle is professor of mathematics at the Universität Heidelberg. His research themes are Galois representations over number and function fields, the arithmetic of function fields, and cohomological methods in positive characteristic. Wolfram Decker is professor of mathematics at TU Kaiserslautern. His research fields are algebraic geometry and computer algebra. He heads the development team of the computer algebra system Singular. From 2010-2016, he was the coordinator of the DFG Priority Program SPP 1489 from which this volume originates. Gunter Malle is professor of mathematics at TU Kaiserslautern. He is working in group representation theory with particular emphasis on algorithmic aspects.