Computational and Algorithmic Problems in Finite Fields
Published on 29. October 2012
Book
Paperback/Softback
XII, 240 pages
978-94-010-4796-8 (ISBN)
Description
'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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1992
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XII, 240 p.
Dimensions
Height: 240 mm
Width: 160 mm
Thickness: 15 mm
Weight
415 gr
ISBN-13
978-94-010-4796-8 (9789401047968)
DOI
10.1007/978-94-011-1806-4
Schweitzer Classification
Other editions
Additional editions
Igor Shparlinski
Computational and Algorithmic Problems in Finite Fields
Book
11/1992
1st Edition
Kluwer Academic Publishers
€105.50
Article exhausted; check different version
Content
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.