[Search][Subject Index][MathMap][Tour][Help!]

	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 11Y: Computational number theory

Introduction

History

Applications and related fields

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).

Subfields

• 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.

Textbooks, reference works, and tutorials

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.

Software and tables

Other web sites with this focus

Selected topics at this site

• 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.