English Dictionary

implicit function

名詞

(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.

日本語の意味

数学解析や代数幾何学の文脈で、(多変数の)暗黙方程式により定義される関数。すなわち、ある変数を関数の値とみなし、その値が他の変数から直接計算できないことが多い。

Near the origin, the implicit function is defined by the equation F(x,y)=0, and its existence follows from the implicit function theorem.

原点付近では、陰関数は方程式F(x,y)=0によって定義され、その存在は陰関数定理から導かれる。

意味（1）

(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. Choosing y as the value means that the implicit function is the inverse of 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.

implicit functions （ plural ）