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- Implicit_function abstract "In mathematics, an implicit equation is a relation of the form R(x1,..., xn) = 0, where R is a function of several variables (often a polynomial). The set of the values of the variables that satisfy this relation is called an implicit curve if n = 2 and an implicit surface if n=3. The implicit equations are the basis of algebraic geometry, whose basic subjects of study are the simultaneous solutions of several implicit equations whose left-hand sides are polynomials. These sets of simultaneous solutions are called affine algebraic sets.For example, the implicit equation of the unit circle is The qualification of implicit for the equation defining a curve or a surface is often used for emphasizing the difference with the definition of a curve or a surface through a parametric equation. Passing from one kind of equation to the other one (for the same curve or surface) is called "implicitization" and "parametrization".An implicit function is a function that is defined implicitly by an implicit equation, by associating one of the variables (the value) to the others (the arguments). For most implicit functions, there is no formula which define them explicitly. Even when such a formula may exist, one must often restrict the domain of definition and the target to have a well defined function. For the example, the implicit equation of the unit circle defines y as a function of x only, if -1 ≤ x ≤ 1 and one considers only non-negative (or non-positive) values for the values of the function.The implicit function theorem provides a condition under which a relation defines an implicit function. It states that if the left hand side of the equation R(x, y) = 0 is differentiable and satisfies some mild condition on its partial derivatives at some point (a, b) such that R(a, b) = 0, then it defines a function y = f(x) over some interval containing a. Geometrically, the graph defined by R(x,y) = 0 will overlap locally with the graph of some equation y = f(x).".
- Implicit_function wikiPageID "250896".
- Implicit_function wikiPageRevisionID "605004476".
- Implicit_function hasPhotoCollection Implicit_function.
- Implicit_function subject Category:Algebraic_geometry.
- Implicit_function subject Category:Differential_calculus.
- Implicit_function subject Category:Differential_topology.
- Implicit_function subject Category:Multivariable_calculus.
- Implicit_function subject Category:Theorems_in_analysis.
- Implicit_function comment "In mathematics, an implicit equation is a relation of the form R(x1,..., xn) = 0, where R is a function of several variables (often a polynomial). The set of the values of the variables that satisfy this relation is called an implicit curve if n = 2 and an implicit surface if n=3. The implicit equations are the basis of algebraic geometry, whose basic subjects of study are the simultaneous solutions of several implicit equations whose left-hand sides are polynomials.".
- Implicit_function label "Función implícita".
- Implicit_function label "Impliciete functie".
- Implicit_function label "Implicit function".
- Implicit_function label "دالة ضمنية".
- Implicit_function label "陰関数".
- Implicit_function label "隐函数".
- Implicit_function sameAs Función_implícita.
- Implicit_function sameAs 陰関数.
- Implicit_function sameAs 음함수와_양함수.
- Implicit_function sameAs Impliciete_functie.
- Implicit_function sameAs m.01l72n.
- Implicit_function sameAs Q1196523.
- Implicit_function sameAs Q1196523.
- Implicit_function wasDerivedFrom Implicit_function?oldid=605004476.
- Implicit_function isPrimaryTopicOf Implicit_function.