英和和英

名詞

algebraic function (複数形 algebraic functions)

1. (algebraic geometry) 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.

   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.

   The value of an algebraic function at an algebraic number is always an algebraic number.

   • 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.

   • 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 ${\displaystyle w=w(z)}$ enables one to determine the polynomial ${\displaystyle P(z,w)}$ up to a constant factor.

   • 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.