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

David R. Kohel

Self-organized criticality (SOC) has become a magic word in various scientific disciplines; it provides a framework for understanding complexity and scale invariance in systems showing irregular fluctuations. In the first 10 years after Per Bak and his co-workers presented their seminal idea, more than 2000 papers on this topic appeared. Seismology has been a field in earth sciences where the SOC concept has already deepened the understanding, but there seem to be much more examples in earth sciences where applying the SOC concept may be fruitful. After introducing the reader into the basics of fractals, chaos and SOC, the book presents established and new applications of SOC in earth sciences, namely earthquakes, forest fires, landslides and drainage networks.

5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002. Proceedings

Algorithmic Number Theory

This book constitutes the refereed proceedings of the 5th International Algorithmic Number Theory Symposium, ANTS-V, held in Sydney, Australia, in July 2002. The 34 revised full papers presented together with 5 invited papers have gone through a thorough round of reviewing, selection and revision. The papers are organized in topical sections on number theory, arithmetic geometry, elliptic curves and CM, point counting, cryptography, function fields, discrete logarithms and factoring, Groebner bases, and complexity.

Claus Fieker

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