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140122 ||| eng |
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|a 9789401118064
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| 100 |
1 |
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|a Shparlinski, Igor
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| 245 |
0 |
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|a Computational and Algorithmic Problems in Finite Fields
|h Elektronische Ressource
|c by Igor Shparlinski
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| 250 |
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|a 1st ed. 1992
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 1992, 1992
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| 300 |
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|a XII, 240 p
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Symbolic and Algebraic Manipulation
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| 653 |
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|a Computer science
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| 653 |
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|a Computer science / Mathematics
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| 653 |
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|a Algebraic fields
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| 653 |
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|a Field Theory and Polynomials
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| 653 |
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|a Theory of Computation
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| 653 |
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|a Polynomials
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Mathematics and its Applications, Soviet Series
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| 028 |
5 |
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|a 10.1007/978-94-011-1806-4
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| 856 |
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|u https://doi.org/10.1007/978-94-011-1806-4?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 512.3
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