Multilínea, dividida

Question

Quiero dividir esta larga ecuación en tres o cuatro (para que quepa en papel A4) manteniendo una alineación con el signo igual. Lo he probado \splity \multlinecodificado, pero todavía no funciona. ¿Tal vez por eso \left[y \right]que encerraba toda la ecuación?

$$
R_i=\Delta_x\Delta_y\left[ \Delta_{1}\Delta_{2}\frac{\partial{\Delta_{21}}}{\partial{w_i}}
+ \Delta_{1}\Delta_{2}\frac{\partial{\Delta_{22}}}{\partial{w_i}}
+ \Delta_{2}\Delta_{1}\frac{\partial{\Delta_{11}}}{\partial{w_i}}
+ \Delta_{2}\Delta_{1}\frac{\partial{\Delta_{12}}}{\partial{w_i}}
- \Delta_{10}\Delta_{20}\Delta_{21}\frac{\partial{\Delta_{11}}}{\partial{w_i}}
- \Delta_{20}\Delta_{20}\Delta_{11}\frac{\partial{\Delta_{21}}}{\partial{w_i}}
- \Delta_{10}\Delta_{20}\Delta_{12}\frac{\partial{\Delta_{22}}}{\partial{w_i}}
- \Delta_{10}\Delta_{20}\Delta_{22}\frac{\partial{\Delta_{12}}}{\partial{w_i}} \right]
$$

Answer 1

Después de recordar que $$nunca debe usarse en LaTeX, consulte¿Por qué es preferible \[ ... \] a $$ ... $$?, aquí hay dos variantes splitque permiten una salida más equilibrada:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
\begin{split}
R_i=\Delta_x\Delta_y
\biggl[
  & \Delta_{1}\Delta_{2}\frac{\partial{\Delta_{21}}}{\partial{w_i}}
  + \Delta_{1}\Delta_{2}\frac{\partial{\Delta_{22}}}{\partial{w_i}}
\\
  &+ \Delta_{2}\Delta_{1}\frac{\partial{\Delta_{11}}}{\partial{w_i}} 
  + \Delta_{2}\Delta_{1}\frac{\partial{\Delta_{12}}}{\partial{w_i}} 
\\
  &- \Delta_{10}\Delta_{20}\Delta_{21}\frac{\partial{\Delta_{11}}}{\partial{w_i}} 
   - \Delta_{20}\Delta_{20}\Delta_{11}\frac{\partial{\Delta_{21}}}{\partial{w_i}} 
\\
  &- \Delta_{10}\Delta_{20}\Delta_{12}\frac{\partial{\Delta_{22}}}{\partial{w_i}}
   - \Delta_{10}\Delta_{20}\Delta_{22}\frac{\partial{\Delta_{12}}}{\partial{w_i}}
\biggr]
\end{split}
\end{equation}

\begin{equation}
\begin{split}
R_i=\Delta_x\Delta_y
\biggl[
  & \Delta_{1}\Delta_{2}\frac{\partial{\Delta_{21}}}{\partial{w_i}}
  + \Delta_{1}\Delta_{2}\frac{\partial{\Delta_{22}}}{\partial{w_i}}
\\
{}+{}& \Delta_{2}\Delta_{1}\frac{\partial{\Delta_{11}}}{\partial{w_i}} 
  + \Delta_{2}\Delta_{1}\frac{\partial{\Delta_{12}}}{\partial{w_i}} 
\\
{}-{}& \Delta_{10}\Delta_{20}\Delta_{21}\frac{\partial{\Delta_{11}}}{\partial{w_i}} 
  - \Delta_{20}\Delta_{20}\Delta_{11}\frac{\partial{\Delta_{21}}}{\partial{w_i}} 
\\
{}-{}& \Delta_{10}\Delta_{20}\Delta_{12}\frac{\partial{\Delta_{22}}}{\partial{w_i}}
  - \Delta_{10}\Delta_{20}\Delta_{22}\frac{\partial{\Delta_{12}}}{\partial{w_i}}
\biggr]
\end{split}
\end{equation}

\end{document}

Answer 2

Una solución ejemplar. Tú elegirás tus lugares de división.

\documentclass{article}
\usepackage{amsmath}
\begin{document}

%$$
\begin{align*}
R_i&=
\Delta_x\Delta_y
%\left[ 
\biggl[
\Delta_{1}\Delta_{2}\frac{\partial{\Delta_{21}}}{\partial{w_i}} 
+  \Delta_{1}\Delta_{2}\frac{\partial{\Delta_{22}}}{\partial{w_i}}
+\Delta_{2}\Delta_{1}\frac{\partial{\Delta_{11}}}{\partial{w_i}} \\
&\qquad
+\Delta_{2}\Delta_{1}\frac{\partial{\Delta_{12}}}{\partial{w_i}} 
-\Delta_{10}\Delta_{20}\Delta_{21}\frac{\partial{\Delta_{11}}}{\partial{w_i}} \\
&\qquad -  \Delta_{20}\Delta_{20}\Delta_{11}\frac{\partial{\Delta_{21}}}{\partial{w_i}}
-  \Delta_{10}\Delta_{20}\Delta_{12}\frac{\partial{\Delta_{22}}}{\partial{w_i}} \\
&\qquad
- \Delta_{10}\Delta_{20}\Delta_{22}\frac{\partial{\Delta_{12}}}{\partial{w_i}} 
\biggr]
%\right]
\end{align*}
%$$

\end{document}

Answer 3

De hecho, no se le permite tener declaraciones no coincidentes \leften \rightlíneas separadas.

Aquí hay una solución que (a) usa \biggl[y \biggr]para crear "vallas" grandes y (b) usa un splitentorno (los tres saltos de línea) anidado dentro de un equationentorno. Según la sugerencia de @egreg, los saltos de línea se eligen para explotar un poco de simetría presente en las expresiones. (Si no le gusta la brecha entre el primer término \biggl[y el primer \Delta_1\Delta_2término, simplemente omita el término \phantom{{}+{}}).

\documentclass{article}
\usepackage{amsmath} % for "split" environment
\begin{document}
\begin{equation}\begin{split}
R_i=\Delta_x\Delta_y\biggl[
&\phantom{{}+{}}\Delta_{1}\Delta_{2}\frac{\partial{\Delta_{21}}}{\partial{w_i}}
 + \Delta_{1}\Delta_{2}\frac{\partial{\Delta_{22}}}{\partial{w_i}} \\
&+ \Delta_{2}\Delta_{1}\frac{\partial{\Delta_{11}}}{\partial{w_i}} 
 +\Delta_{2}\Delta_{1}\frac{\partial{\Delta_{12}}}{\partial{w_i}} \\
&- \Delta_{10}\Delta_{20}\Delta_{21}\frac{\partial{\Delta_{11}}}{\partial{w_i}} 
 - \Delta_{20}\Delta_{20}\Delta_{11}\frac{\partial{\Delta_{21}}}{\partial{w_i}} \\
&-\Delta_{10}\Delta_{20}\Delta_{12}\frac{\partial{\Delta_{22}}}{\partial{w_i}}
-  \Delta_{10}\Delta_{20}\Delta_{22}\frac{\partial{\Delta_{12}}}{\partial{w_i}}\biggr]
\end{split}\end{equation}
\end{document}

Answer 4

Propongo otro diseño (solo 3 líneas) usando el alignedatentorno. Además, una tipificación simplificada de derivadas parciales con el esdiffpaquete:

\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{esdiff}

\begin{document}

\begin{equation}
  \begin{alignedat}{2}
    R_i=\Delta_x\Delta_y
    \biggl[
      & &  \Delta_{1}\Delta_{2}\diffp{\Delta_{21}}{{w_i}}
      + \Delta_{1}\Delta_{2}\diffp{\Delta_{22}}{{w_i}}
      + \Delta_{2}\Delta_{1}\diffp{\Delta_{11}}{{w_i}}
      + \Delta_{2}\Delta_{1}\frac{∂{\Delta_{12}}}{∂{w_i}} &
      \\
      & & - \Delta_{10}\Delta_{20}\Delta_{21}\diffp{\Delta_{11}}{{w_i}}
      - \Delta_{20}\Delta_{20}\Delta_{11}\diffp{\Delta_{21}}{{w_i}} &
      \\
      & & - \Delta_{10}\Delta_{20}\Delta_{12}\diffp{\Delta_{22}}{{w_i}}
      - \Delta_{10}\Delta_{20}\Delta_{22}\diffp{\Delta_{12}}{{w_i}} &
    \biggr]
  \end{alignedat}
\end{equation}

\end{document}