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Riemann-Roch Spaces and Computation / Paraskevas Alvanos.

By: Material type: TextTextLanguage: English Publisher: Warsaw ; Berlin : De Gruyter Open Poland, [2015]Copyright date: ©2015Description: 1 online resource (151 p.)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110426120
Subject(s): Additional physical formats: No title; No titleDDC classification:
  • 510 23
LOC classification:
  • QA333 .A48 2014eb
Online resources:
Contents:
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
Summary: 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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E-Book E-Book De Gruyter Available

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.

Mode of access: Internet via World Wide Web.

This eBook is made available Open Access. Unless otherwise specified individually in the content, the work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license:

https://creativecommons.org/licenses/by-nc-nd/3.0

https://www.degruyter.com/dg/page/open-access-policy

In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Feb 2021)

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