Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory [Hardcover]

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.

Introduction.- B?chle et al: Algorithmic aspects of units in group rings.- M. Barakat et al: A constructice approach to the module of twisted glocal sections on relative projective spaces.- J. B?hm et al: Local to global algorithms for the Gorenstein adjoint ideal of a curve.- M. B?rner et al: Picard curves with small conductor.- W. Bruns et al: Normaliz 2013-2016.- T. Centeleghe et al: Integral Frobenius for abelian varieties with real multiplication.- M. Dettweiler et al: Monodromy of the multiplicative and the additive convolution.- B. Eick et al: Constructing groups of small order: Recent results and open problems.- B. Eick et al: Classifying nilpotent associative algebras: small coclass and fils