¿Cómo puedo enviar esta fórmula por mensaje de texto en LaTeX?

Question



No estoy seguro de cómo enviar mensajes de texto con el isomorfismo con notas en LaTeX. Así muestro la parte de isomorfismo en Latex. Pero no sé cómo agregarle el contenido verde.

\documentclass{article}
\usepackage{amssymb}
\usepackage{tikz}
\newcommand{\quo}[2]{{\raisebox{.2em}{$#1$}\left/\raisebox{-.2em}{$#2$}\right.}} % The quotient of elements or groups
\begin{document}
$\quo{HK}{K}\simeq\quo{H}{H\cap K}$\\
\end{document}

Answer 1

Mira esto, por ejemplo:

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{mathtools}

\newcommand{\quo}[2]{{\raisebox{.2em}{$#1\!$}\left/\raisebox{-.2em}{$#2$}\right.}} % The quotient of elements or groups

\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{calc,tikzmark}
\tikzset{%
    pics/mybraces/.style args={#1/#2}{code={%
            \draw [decorate,decoration={brace,amplitude=4pt,#2},rotate=#1] (0,0) -- (0,1);
    }},
    pics/mybraces/.default=30/{}
} 

\begin{document}
    You can do whatever you want with \LaTeX{}:
    \[
    \underbrace{\quo{\overbrace{HK}^{G}}{K}}_{\mathllap{\mathrm{PGL}(2,\mathbb{C})\text{: projective linear group}}} \simeq \overbrace{\quo{H}{H\cap K}}^{\mathrlap{\mathrm{PSL}(2,\mathbb{C})\text{: projective special linear group}}}\mkern-58mu \underbrace{\phantom{\raisebox{-.2em}{$H\cap K$}}}_{\{\pm I_2\}}
    \]
    You can use also \textbackslash{}\texttt{tikzmark}:
    \[
    \tikzmark{leftpoint}\quo{\overbrace{HK}^{G}}{K} \simeq \quo{H}{H\cap K}\tikzmark{rightpoint}\mkern-58mu \underbrace{\phantom{\raisebox{-.2em}{$H\cap K$}}}_{\{\pm I_2\}}
    \]
    \begin{tikzpicture}[overlay,remember picture]
        \pic at ($(pic cs:leftpoint)+(4pt,-2.5ex)$) {mybraces};
        \node[text width=100pt, align=right] at ($(pic cs:leftpoint)+(-60pt,-1.5ex)$) {$_{\mathrm{PGL}(2,\mathbb{C})\text{:}}$\\ \scriptsize projective linear group};
        \pic at ($(pic cs:rightpoint)+(7pt,-1ex)$) {mybraces={30/mirror}};
        \node[text width=130pt, align=left] at ($(pic cs:rightpoint)+(75pt,3ex)$) {$_{\mathrm{PSL}(2,\mathbb{C})\text{:}}$\\ \scriptsize projective special linear group};
    \end{tikzpicture}%
    However, as Andrew Swan \& Co. already told you, in your case something like this is better:
    \begin{align*} 
        \quo{HK}{K}&\simeq \quo{H}{H\cap K}
        \intertext{where:}
        HK &= G \\
        \intertext{the projective linear group is represented by:} 
        \quo{HK}{K}&= \mathrm{PGL}(2,\mathbb{C}) 
        \intertext{the projective special linear group is represented by:} 
        \quo{H}{H\cap K}&= \mathrm{PSL}(2,\mathbb{C}) 
        \intertext{and} 
        H\cap K&=\{\pm I_2\}
    \end{align*}
\end{document}

Answer 2

Como comenta Andrew Swann, debes explicar la fórmula con algunas palabras. De todos modos, creo que puedes usar esto:

\begin{equation}
    \underbrace{HK}_{G}/\underbrace{K}_{\mathrm{PGL}(2,\mathbb{C})} \simeq \underbrace{H}_{PSL(2,\mathbb{C})}/\underbrace{H\cap K}_{\pm I_2}
\end{equation}