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Header of Algebraic Number

Algebraic number

Definition of the noun algebraic number

What does algebraic number mean as a name of something?


  1. root of an algebraic equation with rational coefficients
    • lexical domain: Quantities - nouns denoting quantities and units of measure
    • more generic terms: irrational / irrational number = a real number that cannot be expressed as a rational number


Algebraic number: In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients. Numbers such as π that are not algebraic are said to be transcendental. Almost all real and complex numbers are transcendental.

  • also known as 代數數

Printed dictionaries and other books with definitions for Algebraic number

Click on a title to look inside that book (if available):

Google previewEncyclopaedia of Mathematics (2012)

by Michiel Hazewinkel

A complex number is called an algebraic number over a field PCC if it is a root of a polynomial (1) with coefficients from P. The minimal polynomial, the degree over P and the conjugate numbers over P for algebraic numbers over P are defined ...

Google previewThe VNR Concise Encyclopedia of Mathematics (2012)

by S. Gottwald

Let } be an algebraic number. The smallest field k = Q(3) that contains Q and also 8 is called an algebraic number field. For example, Q(V3) consists of all numbers of the form a + b V3, where a and b are rational numbers. It is easy to check ...


by McGraw-Hill Education

algebraic number Any root of a polynomial with rational coefficients. { :al-je:bra-ik 'nom-bor } algebraic number field A finite extension field of the field of rational numbers. { :aljoibra-ik 'nom-bor ,feld } algebraic number theory The study of ...

Google previewEncyclopedia of Cryptography and Security (2014)

by Henk C.A. van Tilborg, Sushil Jajodia

Signatures AHS Competition/SHA- Alberti Encryption Algebraic Immunity of Boolean Functions Algebraic Number Field Algorithmic Complexity Attacks Algorithmic DoS Alphabet Android's Security Framework–Understanding the Security ...

Google previewThe Mathematics Dictionary (1992)

by R.C. James, Glenn James

algebraic number. (1) Any ordinary positive or negative number; any real directed number. (2) Any number which is a root of a polynomial equation with rational coefficients; the degree of the polynomial is said to be the ...

Google previewThe New Volumes of the Encyclopaedia Britannica (1902)

Constituting in Combination with the Existing Volumes of the Ninth Edition, the Tenth Edition of that Work, and Also Supplying a New, Distinctive, and Independent Library of Reference Dealing with Recent Events and Developments

Every algebraic number can be expressed in the form osa, where a0 is a natural number and to an algebraic integer; in all that follows it will be supposed that a = 1, and consequently () is integral. Associated with 6 we have a corpus Q = R(0) ...

Google previewThe Encyclopedia Britannica (1922)

a dictionary of arts, sciences, literature and general information by Hugh Chisholm

There is a corresponding theory for the " prime ideals " of the " corpus " associated with any algebraic number. The ana- luguc of Riemann's zeta- function was discovered by R. Dcdekind, but it is only recently that, in the hands of E. Hecke and ...

Google previewThe Century Dictionary: The Century dictionary (1911)

Algebraic number, a root of ...

Google previewThe Century Dictionary and Cyclopedia: The Century dictionary ... prepared under the superintendence of William Dwight Whitney ... rev. & enl. under the superintendence of Benjamin E. Smith (1914)

by William Dwight Whitney, Benjamin Eli Smith

See abundant — Algebraic number, a root of an algebraic equation with whole numbers for its coefficients. -— Alternate, amicable, apocalyptic, appllcate, artificial numbers. See the adjectives. — A number of, several; sometimes, many: as, ...

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Video about Algebraic number

Algebraic number Meaning

Video shows what algebraic number means. A complex number that is a root of a polynomial equation with rational coefficients.. Algebraic number Meaning.

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