algebraic function
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English
[edit]
Noun
[edit]algebraic function (plural algebraic functions)
- (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 enables one to determine the polynomial 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.
Coordinate terms
[edit]Translations
[edit]function definable as the root of some polynomial equation
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