implicit function theorem

Summary

implicit function theorem is a theorem^[1]. It ranks in the top 4% of theorem entities by monthly Wikipedia readership (504 views/month).^[2]

Key Facts

• implicit function theorem's image is recorded as Implicit circle.svg^[3].
• implicit function theorem's instance of is recorded as theorem^[4].
• implicit function theorem's GND ID is recorded as 4570203-2^[5].
• implicit function theorem's part of is recorded as list of theorems^[6].
• implicit function theorem's Freebase ID is recorded as /m/02s4mn^[7].
• implicit function theorem's different from is recorded as inverse function theorem^[8].
• implicit function theorem's statement describes is recorded as implicit function^[9].
• implicit function theorem's defining formula is recorded as \begin{aligned}&f\in\mathcal C^1(\mathbb R^m\times\mathbb R^n,\mathbb R^m)\&\left.\det\frac{\partial f(x,y)}{\partial x}\right|_{(a,b)}\ne0\implies\exists(b\in U\subset\mathbb R^n)\exists(g\colon U\to\mathbb R^n)\colon g(b)=a\land\forall x\in U\colon f(g(x),x)=0\end{aligned}^[10].
• implicit function theorem's studied by is recorded as calculus^[11].
• implicit function theorem's MathWorld ID is recorded as ImplicitFunctionTheorem^[12].
• implicit function theorem's maintained by WikiProject is recorded as WikiProject Mathematics^[13].
• implicit function theorem's Microsoft Academic ID is recorded as 138578839^[14].
• implicit function theorem's OpenAlex ID is recorded as C138578839^[15].
• implicit function theorem's Yale LUX ID is recorded as concept/2a5db441-7cca-4968-b594-d60615d959b3^[16].

Why It Matters

implicit function theorem ranks in the top 4% of theorem entities by monthly Wikipedia readership (504 views/month).^[2] It has Wikipedia articles in 17 language editions, a strong signal of global cultural recognition.^[17] It is known by 9 alternative names across languages and contexts.^[18]