多行、分割

Question

我想將這個長方程式分成三個或四個（以適合 A4 紙）並保持等號對齊。我已經嘗試過\split並\multline編寫了程式碼，但仍然不起作用。也許是因為\left[和\right]包圍了整個方程式？

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

Answer 1

記得$$永遠不要在 LaTeX 中使用後，請參閱為什麼 \[ ... \] 優於 $$ ... $$？，這裡有兩個變體split，可以實現更平衡的輸出：

\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

一個示例性的解決方案。您將選擇分裂的地點​​。

\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

事實上，不允許在單獨的行上有不匹配的\leftand語句。\right

這是一個解決方案，(a) 使用\biggl[和\biggr]建立大型“柵欄”，(b) 使用split嵌套在環境中的環境（三個換行符）equation。根據 @egreg 的建議，選擇換行符號是為了利用表達式中存在的一點對稱性。 （如果您不喜歡\biggl[和 第一項之間的差距\Delta_1\Delta_2，只需省略該術語即可\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

我建議使用環境的另一種佈局（僅3行）alignedat。此外，使用套件簡化了偏導數的類型esdiff：

\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}