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[Texts]## 11Y: Computational number theory |

See also other fields of number theory (section 11). For example, computations of modular square roots are treated in the section of finite fields (11T).

- 11Y05: Factorization
- 11Y11: Primality
- 11Y16: Algorithms; complexity, See also 68Q25
- 11Y35: Analytic computations
- 11Y40: Algebraic number theory computations
- 11Y50: Computer solution of Diophantine equations
- 11Y55: Calculation of integer sequences
- 11Y60: Evaluation of constants
- 11Y65: Continued fraction calculations
- 11Y70: Values of arithmetic functions; tables
- 11Y99: None of the above but in this section

Parent field: 11: Number theory

Browse all (old) classifications for this area at the AMS.

Cohen, Henri: "A course in computational algebraic number theory", Graduate Texts in Mathematics, 138. Springer-Verlag, Berlin, 1993. 534 pp. ISBN 3-540-55640-0 is encyclopedic and readable.

Ribenboim, Paulo: "The new book of prime number records", Springer-Verlag, New York, 1996. 541 pp. ISBN 0-387-94457-5

Riesel, Hans "What's new at the prime number front?" Nordisk Mat. Tidskr. 23 (1975), no. 1, 5--14, 48. MR57#9637

See also the general references for number theory.

- What is the Euclidean algorithm for computing GCDs? [Richard Pinch]
- Improved efficiency of Euclid's algorithm/continued fraction algorithm (for integers or polynomials)
- How to find algebraic relations approximately satisfied by real numbers. (including: LLL routine.)
- Illustration of LLL execution on pari/gp for finding approximate algebraic identities.
- How to execute LLL algorithm in Maple.
- Pointers to LLL (lattice) algorithms and comparison of implementations.
- Examples of bases from which the LLL routine fails to find the minimal basis.
- LLL (and PSLQ) algorithms to find algebraic relations among a set of reals
- Deriving closed-form expressions for infinite sums (experimentally) with PSLQ
- C, perl codes to generate lists of primes
- A [dated] list of available programs for large-integer arithmetic.
- Henri Cohen describes the 2nd edition of his book.
- Hugh Montgomery: software to accompany his number theory text.
- Pointer: free Large Integer Package
- How can one efficiently multiply many-digit numbers?
- List of huge-precision programs and libraries.
- Software pointer: NTL: a C++ library for bignums and algebra over Z and finite fields [Victor Shoup]
- Finding a basis for the nullspace of an integer matrix with small entries.

Last modified 2005/01/14 by Dave Rusin. Mail: