Noun
implicit function (plural implicit functions)
(mathematical analysis, algebraic geometry) A function defined by a (multivariable) implicit equation when one of the variables is regarded as the value of the function, especially where said equation is such that the value is not directly calculable from the other variables.
An important class of implicit functions comprises those defined by equations of the form
x
−
f
(
y
)
=
0
{\displaystyle x-f(y)=0}
. Choosing
y
{\displaystyle y}
as the value means that the implicit function is the inverse of
f
{\displaystyle f}
. This type of implicit function is of particular interest when that inverse is not expressible as a closed-form expression, and thus is difficult to study directly.
I am for richness of meaning rather than clarity of meaning; for the implicit function as well as the explicit function. Robert Venturi
A local embedding theorem is much simpler and can be proved using the implicit function theorem of advanced calculus in a coordinate neighborhood of the manifold. Source: Internet
The proof of the global embedding theorem relies on Nash's far-reaching generalization of the implicit function theorem, the Nash–Moser theorem and Newton's method with postconditioning. Source: Internet
The implicit function theorem converts relations such as into functions. Source: Internet