number field

См. также в других словарях:

• Number Field Sieve — Algorithme de factorisation par crible sur les corps de nombres généralisé En mathématiques, le crible général de corps de nombres est l algorithme, fondé sur l arithmétique modulaire, pour la décomposition en produit de facteurs premiers le plus …   Wikipédia en Français

• number field — noun A field which includes the rational numbers and has finite dimension as a vector space over the rational numbers …   Wiktionary

• number field — noun or number system : the aggregate of all numbers of a given type (as integers, irrationals, complex numbers, vectors) which can be combined by addition or multiplication to obtain a result of the same type …   Useful english dictionary

• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

• General number field sieve — In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 100 digits. Heuristically, its complexity for factoring an integer n (consisting of log2 n bits) is of …   Wikipedia

• Discriminant of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… …   Wikipedia

• Special number field sieve — The special number field sieve (SNFS) is a special purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it.The special number field sieve is efficient for integers of the form r e plusmn; s , where r and …   Wikipedia

• Totally real number field — In number theory, a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers. Equivalent conditions on K , a finite extension of the rational number field Q, are that K is… …   Wikipedia

• Number theory — A Lehmer sieve an analog computer once used for finding primes and solving simple diophantine equations. Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers (the… …   Wikipedia

• Field norm — In mathematics, the (field) norm is a mapping defined in field theory, to map elements of a larger field into a smaller one. Contents 1 Formal definitions 2 Example 3 Further properties 4 See also …   Wikipedia

• Field with one element — In mathematics, the field with one element is a suggestive name for an object that should exist: many objects in math have properties analogous to objects over a field with q elements, where q = 1, and the analogy between number fields and… …   Wikipedia