Computational and Algorithmic Problems in Finite Fields (Mathematics and its Applications) - Softcover
Synopsis
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.
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Computational and Algorithmic Problems in Finite Fields
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -'Et moi, . si j'avait su comment en revenir. je One service mathematics bas rendemI !be n'y semis point a1J6.' human race. It bas put common sense back JulesVeme where it belongs. on tile topmost sbelf next to tile dusty canister labelled 'discarded nonsense'. The series is divergent; therefore we may be Eric T.BeIl able to do something with il O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of pans of mathematics serve as tools for other pans and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics . '; 'One service logic has rendered computer science . '; 'One service category theory has rendered mathematics . .'. All arguably true. And all statements obtainable this way fonn pan of the raison d' 8tre of this series. 256 pp. Englisch. Seller Inventory # 9789401047968
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Computational and Algorithmic Problems in Finite Fields (Mathematics and its Applications)
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Series Editor s Preface. Preface. Notations. Introduction. 1. Polynomial Factorization. 2. Finding Irreducible and Primitive Polynomials. 3. The Distribution of Irreducible and Primitive Polynomials. 4. Bases and Computation in Finite Fields. 5. Coding . Seller Inventory # 5831558
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Computational and Algorithmic Problems in Finite Fields
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -1. Polynomial Factorization.- 1. Univariate factorization.- 2. Multivariate factorization.- 3. Other polynomial decompositions.- 2. Finding irreducible and primitive polynomials.- 1. Construction of irreducible polynomials.- 2. Construction of primitive polynomials.- 3. The distribution of irreducible and primitive polynomials.- 1. Distribution of irreducible and primitive polynomials.- 2. Irreducible and primitive polynomials of a given height and weight.- 3. Sparse polynomials.- 4. Applications to algebraic number fields.- 4. Bases and computation in finite fields.- 1. Construction of some special bases for finite fields.- 2. Discrete logarithm and Zech's logarithm.- 3. Polynomial multiplication and multiplicative complexity in finite fields.- 4. Other algorithms in finite fields.- 5. Coding theory and algebraic curves.- 1. Codes and points on algebraic curves.- 2. Codes and exponential sums.- 3. Codes and lattice packings and coverings.- 6. Elliptic curves.- 1. Some general properties.- 2. Distribution of primitive points on elliptic curves.- 7. Recurrent sequences in finite fields and leyelic linear codes.- 1. Distribution of values of recurrent sequences.- 2. Applications of recurrent sequences.- 3. Cyclic codes and recurrent sequences.- 8. Finite fields and discrete mathematics.- 1. Cryptography and permutation polynomials.- 2. Graph theory, combinatorics, Boolean functions.- 3. Enumeration problems in finite fields.- 9. Congruences.- 1. Optimal coefficients and pseudo-random numbers.- 2. Residues of exponential functions.- 3. Modular arithmetic.- 4. Other applications.- 10. Some related problems.- 1. Integer factorization, primality testing and the greatest common divisor.- 2. Computational algebraic number theory.- 3. Algebraic complexity theory.- 4.Polynomials with integer coefficients.- Appendix 1.- Appendix 2.- Appendix 3.- Addendum.- References.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 256 pp. Englisch. Seller Inventory # 9789401047968
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