Decker W. The Computer Algebra System OSCAR. Algorithms and Examples 2025

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Decker W. The Computer Algebra System OSCAR. Algorithms and Examples 2025

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Textbook in PDF format 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. Preface Acknowledgements List of Contributors OSCAR What Is OSCAR? The Cornerstones Commutative Algebra and Algebraic Geometry Number Theory Group Theory Polyhedral Geometry Applications Algorithms for Gromov–Witten Invariants of Elliptic Curves Toric Geometry Algorithms for GIT-Fans of Affine Torus Actions Elliptic Fibrations on Vinberg’s Most Algebraic K3 Surface An Atlas of Orthogonal Representations Gröbner Bases for Polynomial Ideals andApplications Invariant Theory Monomial Bases in Lie Theory Matroids Generic Root Counts of Tropically Transverse Systems Faithful Tropicalization of Hyperelliptic Curves Tropical Implicitization Revisited F-Theory Applications Confirmable Workflows