Standardfunktion

Standardfunktion, in German-language texts often written as Standardfunktion, denotes a canonical set of functions regarded as fundamental building blocks in mathematics and computer science. The term is used in different contexts, sometimes synonymously with elementary functions in mathematics, and sometimes as a label for functions provided by a language’s standard library in programming. The precise scope depends on discipline and author.

In mathematics, standard functions typically include the elementary functions: polynomial and rational functions; root and power functions; exponentials and logarithms; trigonometric and inverse trigonometric functions; hyperbolic and inverse hyperbolic functions; absolute value and common piecewise-defined functions. They are characterized by well-known domains, basic algebraic properties, and a rich set of calculus rules, enabling composition, limits, series, and differentiation or integration. They serve as universal building blocks for defining more complex functions.

In computer science, standard functions usually refer to the functions provided by a language’s standard library. These functions offer common operations such as arithmetic, exponentiation, square root, trigonometric calculations, logarithms, as well as string handling, input/output and memory management utilities. They are designed to be portable across platforms and are typically optimized for performance and numerical stability.

Because the term is not tied to a single formal definition, its meaning is contextual. In mathematics it points to a minimal, well-understood set of functions; in programming it refers to the officially supplied set of routines. See also Elementary function; Standard library; Function (mathematics).