In mathematics, the term "characteristic function" can refer to any of several distinct concepts: The indicator function of a subset, that is the function 1 A : X → { 0, 1 }, {\displaystyle \mathbf {1} _{A}\colon X\to \{0,1\},} which for a given subset A of X, has value 1 at points of A and 0 at points of X − A.There is an indicator function for affine varieties over a finite field: given a finite set of functions f α ∈ F q [ x 1, …, x n ] {\displaystyle f_{\alpha }\in \mathbb {F} _{q}[x_{1},\ldots,x_{n}]} let V = { x ∈ F q n : f α = 0 } {\displaystyle V=\left\{x\in \mathbb {F} _{q}^{n}:f_{\alpha }=0\right\}} be their vanishing locus. Wikipedia