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real number field

См. также в других словарях:

  • 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

  • Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …   Wikipedia

  • Real number — For the real numbers used in descriptive set theory, see Baire space (set theory). For the computing datatype, see Floating point number. A symbol of the set of real numbers …   Wikipedia

  • real number system — noun The complete ordered field (of real numbers). See Also: real number line …   Wiktionary

  • 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

  • Definable real number — A real number a is first order definable in the language of set theory, without parameters, if there is a formula φ in the language of set theory, with one free variable, such that a is the unique real number such that φ(a) holds in the standard… …   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

  • Extended real number line — Positive infinity redirects here. For the band, see Positive Infinity. In mathematics, the affinely extended real number system is obtained from the real number system R by adding two elements: +∞ and −∞ (read as positive infinity and negative… …   Wikipedia

  • Real algebraic geometry — In mathematics, real algebraic geometry is the study of real number solutions to algebraic equations with real number coefficients.Real plane curvesSince the real number field is not algebraically closed, the geometry of even a plane curve C in… …   Wikipedia

  • Real field — may refer to: * Real numbers, the numbers that can be represented by infinite decimals * Formally real field, an algebraic field that has the so called real property …   Wikipedia

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