Computational Arithmetic Geometry
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Computational Arithmetic Geometry
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Author : Kristin Estella Lauter
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Computational Arithmetic Geometry written by Kristin Estella Lauter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Algebraic number theory categories.
With the recent increase in available computing power, new computations are possible in many areas of arithmetic geometry. To name just a few examples, Cremona's tables of elliptic curves now go up to conductor 120,000 instead of just conductor 1,000, tables of Hilbert class fields are known for discriminant up to at least 5,000, and special values of Hilbert and Siegel modular forms can be calculated to extremely high precision. In many cases, these experimental capabilities haveled to new observations and ideas for progress in the field. They have also led to natural algorithmic questions on the feasibility and efficiency of many computations, especially for the purpose of applications in cryptography. The AMS Special Session on Computational Arithmetic Geometry, held onApril 29-30, 2006, in San Francisco, CA, gathered together many of the people currently working on the computational and algorithmic aspects of arithmetic geometry. This volume contains research articles related to talks given at the session. The majority of articles are devoted to various aspects of arithmetic geometry, mainly with a computational approach.
Arithmetic Geometry Number Theory And Computation
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Author : Jennifer S. Balakrishnan
language : en
Publisher: Springer Nature
Release Date : 2022-03-15
Arithmetic Geometry Number Theory And Computation written by Jennifer S. Balakrishnan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-15 with Mathematics categories.
This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research. Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Computing In Algebraic Geometry
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Author : Wolfram Decker
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-01
Computing In Algebraic Geometry written by Wolfram Decker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-01 with Mathematics categories.
This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.
Computational Methods In Commutative Algebra And Algebraic Geometry
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Author : Wolmer Vasconcelos
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-18
Computational Methods In Commutative Algebra And Algebraic Geometry written by Wolmer Vasconcelos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-18 with Mathematics categories.
This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.
Computational Geometry
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Author : Franco P. Preparata
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computational Geometry written by Franco P. Preparata and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
Computational Algebraic Geometry
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Author : Frederic Eyssette
language : en
Publisher: Birkhäuser
Release Date : 2011-11-25
Computational Algebraic Geometry written by Frederic Eyssette and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-25 with Mathematics categories.
Computational Aspects Of Modular Forms And Galois Representations
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Author : Bas Edixhoven
language : en
Publisher: Princeton University Press
Release Date : 2011-06-20
Computational Aspects Of Modular Forms And Galois Representations written by Bas Edixhoven and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-20 with Mathematics categories.
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Issues In Logic Operations And Computational Mathematics And Geometry 2011 Edition
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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2012-01-09
Issues In Logic Operations And Computational Mathematics And Geometry 2011 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-09 with Mathematics categories.
Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Robust And Error Free Geometric Computing
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Author : Dave Eberly
language : en
Publisher: CRC Press
Release Date : 2021-02-28
Robust And Error Free Geometric Computing written by Dave Eberly and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-28 with Computers categories.
This is a how-to book for solving geometric problems robustly or error free in actual practice. The contents and accompanying source code are based on the feature requests and feedback received from industry professionals and academics who want both the descriptions and source code for implementations of geometric algorithms. The book provides a framework for geometric computing using several arithmetic systems and describes how to select the appropriate system for the problem at hand. Key Features: A framework of arithmetic systems that can be applied to many geometric algorithms to obtain robust or error-free implementations Detailed derivations for algorithms that lead to implementable code Teaching the readers how to use the book concepts in deriving algorithms in their fields of application The Geometric Tools Library, a repository of well-tested code at the Geometric Tools website, https://www.geometrictools.com, that implements the book concepts
Ideals Varieties And Algorithms
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Author : David A Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-31
Ideals Varieties And Algorithms written by David A Cox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-31 with Mathematics categories.
This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: a significantly updated section on Maple; updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; and presents a shorter proof of the Extension Theorem.