$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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Let $U\subseteq\mathbb{R}^{n+m}$ be open and let $\phi:U\to\mathbb{R}^p$. Suppose $\vec{x}\in\mathbb{R}^n$, $\vec{y}\in\mathbb{R}^m$, satisfying $\phi(\vec{x}, \vec{y})=\vec{0}$. This equation defines an implicit relationship between $\vec{x}$ and $\vec{y}$.

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Let $U\subseteq\mathbb{R}^{n+m}$ be open and let $\phi:U\to\mathbb{R}^p$. Suppose $\vec{x}\in\mathbb{R}^n$, $\vec{y}\in\mathbb{R}^m$, satisfying $\phi(\vec{x}, \vec{y})=\vec{0}$. This equation defines an implicit relationship between $\vec{x}$ and $\vec{y}$.

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definition
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definition
concepts
used in
hypothesis
results
Let $U\subseteq\mathbb{R}^{n+m}$ be open and let $\phi:U\to\mathbb{R}^p$. Suppose $\vec{x}\in\mathbb{R}^n$, $\vec{y}\in\mathbb{R}^m$, satisfying $\phi(\vec{x}, \vec{y})=\vec{0}$. This equation defines an implicit relationship between $\vec{x}$ and $\vec{y}$.

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Let $U\subseteq\mathbb{R}^{n+m}$ be open and let $\phi:U\to\mathbb{R}^p$. Suppose $\vec{x}\in\mathbb{R}^n$, $\vec{y}\in\mathbb{R}^m$, satisfying $\phi(\vec{x}, \vec{y})=\vec{0}$. This equation defines an implicit relationship between $\vec{x}$ and $\vec{y}$.

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