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Friday, November 13, 2020 | History

3 edition of Computational aspects of algebraic curves found in the catalog.

Computational aspects of algebraic curves

Computational aspects of algebraic curves

University of Idaho, USA, 26-28 May 2005

by

  • 181 Want to read
  • 33 Currently reading

Published by World Scientific in Singapore, Hackensack, N.J .
Written in English

    Subjects:
  • Curves, Algebraic -- Data processing -- Congresses.,
  • Geometry, Algebraic -- Data processing -- Congresses.

  • Edition Notes

    Statementeditor, Tanush Shaska.
    GenreCongresses.
    SeriesLecture notes series on computing -- vol. 13
    ContributionsShaska, Tanush.
    Classifications
    LC ClassificationsQA565 .C6 2005
    The Physical Object
    Paginationxi, 272 p. :
    Number of Pages272
    ID Numbers
    Open LibraryOL22721407M
    ISBN 109812564594


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Computational aspects of algebraic curves Download PDF EPUB FB2

The main goal of the book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography.

The main goal of this book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography.

Tanush Shaska is the author of Computational Aspects of Algebraic Curves ( avg rating, 1 rating, 0 reviews, published ), Lecture Notes in Linear 5/5(1). Aims to highlight computational techniques related to algebraic curves.

This book covers topics in this area, including elliptic curve cryptography, hyper elliptic curves, representations on some Riemann-Roch spaces of modular curves, computation of Hurwitz spectra, generating systems of finite groups, and Galois groups of polynomials.

System Upgrade on Tue, May 19th, at 2am (ET) During this period, E-commerce and registration of new users may not be available for up to 12 hours.

Algebraic curves and surfaces combine fas- nating mathematical beauty with challenging computational complexity and wide spread practical applicability.

In this book we treat only algebraic curves, although many of the results and methods can be and in fact have been generalized to surfaces. Being the solution loci of algebraic, i. Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications.

It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and.

Lecture Notes Series on Computing Computational Aspects of Algebraic Curves, pp. () No Access Hyperelliptic curves of genus 3 with. Computational Geometry: Curve and Surface Modeling provides information pertinent to the fundamental aspects of computational geometry.

This book discusses the geometric properties of parametric polynomial curves by using the theory of affine invariants for algebraic curves. The main goal of this book is to highlight such computational techniques related to algebraic curves.

The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography Price: $   In Márquez-Corbella et al.

() – for so called very strong algebraic geometry codes C = Computational aspects of algebraic curves book L (X, P, E), where X is an algebraic curve over F q, P is an n-tuple of mutually distinct F q-rational points of X and E is a divisor of X with disjoint support from P – it was shown that an equivalent representation C = C L (Y, Q, F) can be found.

ISBN: OCLC Number: Notes: "University of Idaho, USA, May " Description: xi, pages ; 24 cm. Contents: A new proof for the non-degeneracy of the Frey-Rück pairing and a connection to isogenies over the base field / E.F.

Schaefer --Elliptic curve torsion points and division polynomials / I.A. Burhanuddin and M.A. Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

The fundamental objects of study in algebraic geometry are algebraic varieties, which are. Get this from a library.

Computational aspects of algebraic curves, University of Idaho, USA, May [Tanush Shaska;] -- The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry.

The main goal of this book is to highlight. Algebraic, analytic, and geometric methods are used to study algebraic curves and Riemann surfaces from a variety of points of view. The object of the study is the same.

Graduate students and research mathematicians interested in computational aspects of algebraic and analytic geometry. Access this eBook now. Book Series Name. This volume contains complete texts of the lectures held during the Summer School on "Computational Aspects of Model Choice" orga nized jointly by Charles University, Prague, and International Associa tion for Statistical Computing (IASC) on July, in Prague.

Main aims of the Summer School were to review and analyse some of the recent. COMPUTATIONAL ASPECTS OF CURVES OF GENUS AT LEAST 2 3 singularities are unavoidable if one wishes to remain in the plane, since the genus of a nonsingular plane curve of degree d is (d−1)(d−2)/2 6= 2.

A curve X is hyperelliptic if it admits a map to P1 over k and its genus is at least 2. Computational aspects of algebraic curves. Papers from the conference held at the University of Idaho, Moscow, ID, May 26–28, Edited by Tanush Shaska. Lecture Notes Series on Computing, World Scientific Publishing Co.

Pte. Ltd., Hackensack, NJ, xii+ pp. The other book suggestions are all so far excellent; the only caveat with them is that they all get into the number theoretic aspects very soon.

I am taking the guess that you are more geometrically minded since you are starting with algebraic geometry rather than. Seppälä, MSimple numerical uniformization of elliptic curves. in T Shaska (ed.), Computational aspects of algebraic curves. Lecture notes series on computing, vol.

13, pp.Conference on Computational Aspects of Algebraic Curves, Moscow, Idaho, United States, 26/05/   Algebraic Curves and Finite Fields: Cryptography and Other Applications (Radon Series on Computational and Applied Mathematics 16) They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.

The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 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.

Rick Miranda's Algebraic Curves and Riemann Surfaces is a great place to look for a more complex analytic point of view. I think it starts from very little and only asks you know a bit of complex analysis.

See here for a review of this book by Gunning. As David Lehavi has already recommended in the comments, Herbert Clemens's A Scrapbook of Complex Curve Theory is.

An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision.

Requiring no prior experience with number theory or sophisticated algebraic tools, the book covers many computational aspects of number theory and highlights important and interesting engineering applications.

It first builds the foundation of computational number theory by covering the arithmetic of integers and polynomials at a very basic level. In book: Computational Methods for Algebraic Spline Surfaces, pp to the geometrical aspects of mathematics and computer sciences.

parameterization of real space algebraic curves. This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book.

A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology.

Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. The case of elliptic curves (Schoof’s algorithm) was at the birth of elliptic curve cryptography around 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. The book's major energies are devoted to the current hot topics in computational number theory — elliptic curves, Hermite normal forms, sub-exponential algorithms, number field sieves, factoring and primality testing, LLL algorithms, and the bread-and-butter number field computations including computations of regulators, fundamental units and.

The book is the first comprehensive monograph on the level of a graduate textbook to systematically cover the fundamental aspects of the emerging discipline of computational geometry.

It is written by founders of the field and the first edition covered all major developments in the preceding 10 years. This book is intended to provide material for a graduate course of one or two semesters on computational commutative algebra and algebraic geometry spotlighting potential applications in cryptography.

Conference on Computational Aspects of Algebraic Curves, University of Idaho, May(supported by NSA) Special session, AMS annual meeting: Algorithmic Algebraic and Analytic Geometry, Atlanta, JanuaryComputational Aspects of Algebraic Curves, ACA Computational Aspects of Algebraic Curves, ACARaleigh, NC State.

A Wolfram Language Approach to Real Numerical Algebraic Plane Curves» This article is a summary of my book A Numerical Approach to Real Algebraic Curves with the Wolfram Language. we discuss computational aspects of the recently introduced Newton and Weierstrass methods for finding the roots of a quaternionic polynomial.

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field.

Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications.

The first two papers are prefatory, aspiring to lure the reader into following the subject more profoundly. The next eight papers address important topics in the field: smooth numbers, factoring, primality, lattices, elliptic curves, algebraic.

ISSAC ' Proceedings of the on International Symposium on Symbolic and Algebraic Computation. New bounds for lower envelopes in three dimensions, with applications to visibility in terrains.

coding theory; cryptography. msc |Algebraic geometry – Arithmetic problems. Diophantine ge-ometry – Zeta-functions and related questions. msc |Algebraic geometry – Computational aspects in algebraic geometry – Curves. msc |Group theory and generalizations – Representation theory.

The aim of this programme is to provide the series of lectures on computational aspects of algebraic geometry. The lectures will be accompanied with computational Magma sessions.

The programme will include: Mini course on GPU programming and applications (by Zvonimir Bujanović) Computing the Picard lattice of a genus two K3 surface (by Dino Festi).Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach - Ebook written by William Stein.

Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Elementary Number Theory: Primes, Congruences, and Secrets: A Computational .This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology.

Each chapter fully details and provides a tutorial introduction to important concepts and results.