Frontmatter -- Contents -- Preface -- Part I: Riemann-Roch Spaces -- 1 Elements of Algebra -- 2 Function Fields and Curves -- 3 Riemann-Roch Spaces -- 4 Integral Domains -- Part II: Computation -- 5 Computing Integral Bases -- 6 Computing Riemann-Roch Spaces -- 7 Computing Resultant and Norm Form Equations -- 8 Computing Integral Points on Rational Curves -- Appendices -- Bibliography -- Index -- Index of Algorithms
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The book focuses on the educational perspective of Riemann-Roch spaces and the computation of algebraic structures connected to the Riemann-Roch theorem, which is a useful tool in fields of complex analysis and algebraic geometry. On one hand, the theorem connects the Riemann surface with its topological genus, and on the other it allows us to compute the algebraic function field spaces. In the first part of this book, algebraic structures and some of their properties are presented. The second part shows efficient algorithms and examples connected to Riemann-Roch spaces. What is important, a variety of examples with codes of algorithms are given in the book, covering the majority of the cases.
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