Last edited by Tajora
Friday, May 8, 2020 | History

1 edition of Computational and Algorithmic Problems in Finite Fields found in the catalog.

Computational and Algorithmic Problems in Finite Fields

by Igor E. Shparlinski

  • 140 Want to read
  • 30 Currently reading

Published by Springer Netherlands in Dordrecht .
Written in English

    Subjects:
  • Mathematics,
  • Information theory,
  • Field theory (Physics),
  • Data processing,
  • Algebra

  • About the Edition

    This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.

    Edition Notes

    Statementby Igor E. Shparlinski
    SeriesMathematics and Its Applications (Soviet Series) -- 88, Mathematics and Its Applications (Soviet Series) -- 88
    Classifications
    LC ClassificationsQA161.A-161.Z, QA161.P59
    The Physical Object
    Format[electronic resource] /
    Pagination1 online resource (xii, 240 p.)
    Number of Pages240
    ID Numbers
    Open LibraryOL27025679M
    ISBN 109401047960, 940111806X
    ISBN 109789401047968, 9789401118064
    OCLC/WorldCa851387419

    Book Description. Developed from the author’s popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in . Computational Mathematics involves mathematical research in areas of science and engineering where computing plays a central and essential role. Topics include for example developing accurate and efficient numerical methods for solving physical or biological models, analysis of numerical approximations to differential and integral equations, developing computational tools to.

    Computational Geometry Algorithms And Applications. Welcome,you are looking at books for reading, the Computational Geometry Algorithms And Applications, you will able to read or download in Pdf or ePub books and notice some of author may have lock the live reading for some of ore it need a FREE signup process to obtain the book. We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding theory, algebraic symbol manipulation, and number by:

    Algorithmic number theory Sample problems include the discrete logarithm problem, systems of polynomials (linear and nonlinear), factoring integers and polynomials (univariate and multivariate), primary decomposition, decoding of algebraic geometry codes, quantum algorithms for the hidden subgroup problem, reverse engineering of gene networks.   Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas.


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Computational and Algorithmic Problems in Finite Fields by Igor E. Shparlinski Download PDF EPUB FB2

Computational and Algorithmic Problems in Finite Fields Computational and Algorithmic Problems in Finite Fields. Authors: Shparlinski, Igor Free Preview. *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis.

ebook access is temporary and does not include ownership of the ebook. Only Brand: Springer Netherlands. Computational and Algorithmic Problems in Finite Fields. Authors (view affiliations) Igor E. Shparlinski; Part of the Mathematics and Its Applications (Soviet Series) book series (MASS, volume 88) Log in to check access.

Buy eBook. USD Buy eBook. USD Recurrent Sequences in Finite Fields and Cyclic Linear Codes. Igor E. A treatment of computation and algorithms for finite fields.

The book covers such topics as polynomial factorization, distribution of primitive polynomials and of primitive points on elliptic curves, Read more. This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics.

Finite Fields | This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics.

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of : Springer Netherlands.

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases Price: $ This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite.

1) an abstract (or a proper) computational algorithm applicable to mathematical objects (elements of finite-dimensional vector spaces, fields, algebraic systems, functional systems, etc.) which is independent of the particular computer used and which may be written down in conventional mathematical terms or in some algorithmic language.

Areas of application include but are not limited to algebraic coding theory, cryptology, and combinatorial design theory.

Computational and algorithmic aspects of finite field problems are also growing in significance. The conference drew workers in theoretical, applied, and algorithmic finite field theory.

All papers were : and Algorithms (4th: University of Waterloo) International Conference on Finite Fields: Theory, Applications. Computational complexity theory focuses on classifying computational problems according to their inherent difficulty, and relating these classes to each other.

A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm.

A problem is regarded as inherently difficult if its solution requires. “Symbolic Computational Algebra” at New York University. A rough set of class-notes grew out of this class and evolved into the following final form at an excruciatingly slow pace over the last five years.

This book also benefited from the comments and experience of several people, some ofFile Size: 2MB. Computational and algorithmic aspects of finite field problems are also growing in significance. The conference drew workers in theoretical, applied, and algorithmic finite field theory.

All papers were refereed. They are loosely classified as theoretical and applied and Author: and Algorithms (4th: University of Waterloo) International Conference on Finite Fields: Theory, Applications, Ronald C.

Mullin, Gary L. Mullen. Reviewed by William McGovern, Professor, University of Washingon on 8/21/ Comprehensiveness rating: 5 see less.

As promised by the title, the book gives a very nice overview of a side range of topics in number theory and algebra (primarily the former, but with quite a bit of attention to the latter as well), with special emphasis to the areas in which computational techniques have proved /5(3).

This paper provides an algorithmic approach to some basic algebraic and combinatorial properties of algebraic curves over finite fields: the number of points on a curve or a projection, its number. So, it turns out that PSPACE = NPSPACE.

My complexity professor described it as memory being "more powerful" than computation because you can reuse memory. This means that any examples taking NP-space can be done in just polynomial space.

Rememb. Algorithmic Problems in Computational Structural Biology. which actually subsumes two related problems: the way a protein adopts its D structure —folding, and the way two or several.

Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August at the University of Nevada at Las Vegas.

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry.

It may serve as a reference and study guide to the field. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice.

Preferably the book should have many examples of how to formulate computational problems rigorously from various domain and real world examples. Clarification To make the question more specific, let's assume that they know basic math/CS terminology like sets, functions, graphs, lists, etc.

at the level of 1st/2nd year undergraduate CS student.Computational and Algorithmic Problems in Finite Fields, I. Shparlinski, Kluwer, A catalog of open problems and references. Like [Guy94], this is a reference, not a text.

($, UMd library) Solved and Unsolved Problems in Number Theory, 3 nd Ed, D. Shanks, Chelsea, In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ()) is a finite sequence of well-defined, computer-implementable instructions, typically to solve a class of problems or to perform a computation.

Algorithms are always unambiguous and are used as specifications for performing calculations, data processing, automated reasoning, and other tasks.