In algebraic geometry, a regular function on an open subset of an algebraic variety is a function that can be expressed locally as a quotient of polynomials, with nonzero on the neighborhood in question. More generally, regular functions on a scheme are the sections of its structure sheaf.

In older complex-analysis terminology, a function is termed regular iff it is analytic and single-valued throughout a region .

See also

Analytic Function, Holomorphic Function, Rational Function, Single-Valued Function, Structure Sheaf

Portions of this entry contributed by Adam Getchell

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References

Hartshorne, R. Algebraic Geometry. New York: Springer-Verlag, pp. 15-16, 1977.Mathews, J. and Walker, R. L. Mathematical Methods of Physics, 2nd ed. Reading, MA: W. A. Benjamin/Addison-Wesley, p. 477, 1970.

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Regular Function

Cite this as:

Weisstein, Eric W., with contributions by Adam Getchell. "Regular Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RegularFunction.html

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