Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
Editors: Böckle, Gebhard, Decker, Wolfram, Malle, Gunter (Eds.)
- Broad range of up to date computational recipes
- Introduction to computational tools by explicit examples
- Applications from providing new examples to solving classification problems
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- About this book
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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.
- About the authors
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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.
- Table of contents (31 chapters)
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Algorithmic Aspects of Units in Group Rings
Pages 1-22
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A Constructive Approach to the Module of Twisted Global Sections on Relative Projective Spaces
Pages 23-49
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Local to Global Algorithms for the Gorenstein Adjoint Ideal of a Curve
Pages 51-96
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Picard Curves with Small Conductor
Pages 97-122
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Normaliz 2013–2016
Pages 123-146
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Table of contents (31 chapters)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
- Editors
-
- Gebhard Böckle
- Wolfram Decker
- Gunter Malle
- Copyright
- 2017
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG, part of Springer Nature
- eBook ISBN
- 978-3-319-70566-8
- DOI
- 10.1007/978-3-319-70566-8
- Hardcover ISBN
- 978-3-319-70565-1
- Softcover ISBN
- 978-3-030-09969-5
- Edition Number
- 1
- Number of Pages
- IX, 763
- Number of Illustrations
- 97 b/w illustrations, 16 illustrations in colour
- Topics
