Dictionary

algebraic function en · NOUN

Meanings

1. Informally, any function expressible using (only) the operations of addition, subtraction, multiplication, division and raising to a rational power; more precisely, any continuous function definable as the root of some polynomial equation.
   • The value of an algebraic function at an algebraic number is always an algebraic number.
   • 1992, A. A. Goldberg, V. A. Pyana, Uniqueness Theorems for Algebraic Functions, A. B. Sossinsky (translation editor), Boris Yakovlevich Levin (editor), Entire and Subharmonic Functions, American Mathematical Society, page 199, It is known that the algebraic function w=w(z) enables one to determine the polynomial P(z,w) up to a constant factor.
   • 1989, Manuel Bronstein, An Algorithm for the Integration of Elementary Functions, James H. Davenport (editor), EUROCAL '87: European Conference on Computer Algebra, Proceedings, Springer, LNCS 378, page 491, Trager (1984) recently gave a new algorithm for the indefinite integration of algebraic functions.
   • Quite often, algebraic functions are algebraic expressions using a finite number of terms and involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Some algebraic functions, however, cannot be expressed by such finite expressions.
   • 1993, Goro Kato (translator), Kenkichi Iwasawa, Algebraic Functions, American Mathematical Society, page xiv, Riemann provided a clear picture of many difficult topics. His most significant contribution, rather than his construction of a Riemann surface from an algebraic function, was to derive the existence of algebraic functions as he built his theory based on the concept of a Riemann surface.

Forms

Coordinates

transcendental function

Relateds

algebraic variety · algebraic number

Translations (8)

de algebraische Funktion (function definable as the root of some polynomial equation) · cs algebraická funkce (function definable as the root of some polynomial equation) · fr fonction algébrique (function definable as the root of some polynomial equation) · sh algebarska funkcija (function definable as the root of some polynomial equation) · ru алгебраическая функция (function definable as the root of some polynomial equation) · es función algebraica (function definable as the root of some polynomial equation) · pt função algébrica (function definable as the root of some polynomial equation) · sv algebraisk funktion (function definable as the root of some polynomial equation)