使用systeme时如何将方程组宽度调整至段落宽度

问题背景 #

需要将大型微分方程组适配JASSS文档的段落宽度，当前用scriptsize缩小公式的方法因幅度过大效果不佳，原代码如下：

\documentclass{JASSS}
\usepackage{array}
\usepackage{amsmath,systeme}
\usepackage{tabularx,colortbl}
\usepackage{booktabs}
\newcolumntype{M}[1]{p{#1}}
\begin{document}
\begin{equation}
\systeme{
\frac{dA_1}{dt}= \mu_1 N_1 - k_{B} p_{B} A_1 \frac{B}{N_1} - (1-k_{B} p_{B}) k_{D} p_{D} A_1 \frac{D}{N_2} - k_{C} p_{C} A_1 \frac{C}{N_1} - (1-k_{C} p_{C}) k_{E} p_{E} A_1 \frac{E}{N_2} - \mu_{A_1} A_1 + \gamma_{B} B + \gamma_{C} C ,  
\frac{dB}{dt}= k_{B} p_{B} A_1 \frac{B}{N_1} + (1-k_{B} p_{B}) k_{D} p_{D} A_1 \frac{D}{N_2} - \phi_{C} B \frac{C}{N_1} - (1-\phi_{C}) \phi_{E} B \frac{E}{N_2} + \phi_{B} C \frac{B}{N_1} + (1-\phi_{B}) \phi_{D} C \frac{D}{N_2} - \mu_{B} B - \gamma_{B} B ,
\frac{dC}{dt}= k_{C} p_{C} A_1 \frac{C}{N_1} + (1-k_{C} p_{C}) k_{E} p_{E} A_1 \frac{E}{N_2} - \phi_{B} C \frac{B}{N_1} - (1-\phi_{B}) \phi_{D} C \frac{D}{N_2} + \phi_{C} B \frac{C}{N_1} + (1-\phi_{C}) \phi_{E} B \frac{E}{N_2} - \mu_{C} C - \gamma_{C} C ,
\frac{dA_2}{dt}=\mu_2 N_2 - k_{D} p_{D} A_2 \frac{D}{N_2} - (1-k_{D} p_{D}) k_{B} p_{B} A_2 \frac{B}{N_1} - k_{E} p_{E} A_2 \frac{E}{N_2} - (1-k_{E} p_{E}) k_{C} p_{C} A_2 \frac{C}{N_1} - \mu_{A_2} A_2 + \gamma_{D} D + \gamma_{E} E ,
\frac{dD}{dt}= k_{D} p_{D} A_2 \frac{D}{N_2} + (1-k_{D} p_{D}) k_{B} p_{B} A_2 \frac{B}{N_1} - \phi_{E} D \frac{E}{N_2} - (1-\phi_{E}) \phi_{C} D \frac{C}{N_1} + \phi_{D} E \frac{D}{N_2} + (1-\phi_{D}) \phi_{B} E \frac{B}{N_1} - \mu_{D} D - \gamma_{D} D ,
\frac{dE}{dt}= k_{E} p_{E} A_2 \frac{E}{N_2} + (1-k_{E} p_{E}) k_{C} p_{C} A_2 \frac{C}{N_1} - \phi_{D} E \frac{D}{N_2} - (1-\phi_{D}) \phi_{B} E \frac{B}{N_1} + \phi_{E} D \frac{E}{N_2} + (1-\phi_{E}) \phi_{C} D \frac{C}{N_1} - \mu_{E} E - \gamma_{E} E }
\end{equation}
\end{document}

可行解决方案 #

1. 拆分长方程为多行（推荐）

利用amsmath的split环境与systeme结合，将每个过长的方程拆分为多行，保持字号不变，仅调整换行位置以适配宽度：

\documentclass{JASSS}
\usepackage{array}
\usepackage{amsmath,systeme}
\usepackage{tabularx,colortbl}
\usepackage{booktabs}
\newcolumntype{M}[1]{p{#1}}
\begin{document}
\begin{equation}
\systeme{
\begin{split}
\frac{dA_1}{dt} &= \mu_1 N_1 - k_{B} p_{B} A_1 \frac{B}{N_1} - (1-k_{B} p_{B}) k_{D} p_{D} A_1 \frac{D}{N_2} \\
&\quad - k_{C} p_{C} A_1 \frac{C}{N_1} - (1-k_{C} p_{C}) k_{E} p_{E} A_1 \frac{E}{N_2} \\
&\quad - \mu_{A_1} A_1 + \gamma_{B} B + \gamma_{C} C ,
\end{split}
\begin{split}
\frac{dB}{dt} &= k_{B} p_{B} A_1 \frac{B}{N_1} + (1-k_{B} p_{B}) k_{D} p_{D} A_1 \frac{D}{N_2} \\
&\quad - \phi_{C} B \frac{C}{N_1} - (1-\phi_{C}) \phi_{E} B \frac{E}{N_2} \\
&\quad + \phi_{B} C \frac{B}{N_1} + (1-\phi_{B}) \phi_{D} C \frac{D}{N_2} - \mu_{B} B - \gamma_{B} B ,
\end{split}
\begin{split}
\frac{dC}{dt} &= k_{C} p_{C} A_1 \frac{C}{N_1} + (1-k_{C} p_{C}) k_{E} p_{E} A_1 \frac{E}{N_2} \\
&\quad - \phi_{B} C \frac{B}{N_1} - (1-\phi_{B}) \phi_{D} C \frac{D}{N_2} \\
&\quad + \phi_{C} B \frac{C}{N_1} + (1-\phi_{C}) \phi_{E} B \frac{E}{N_2} - \mu_{C} C - \gamma_{C} C ,
\end{split}
\begin{split}
\frac{dA_2}{dt} &= \mu_2 N_2 - k_{D} p_{D} A_2 \frac{D}{N_2} - (1-k_{D} p_{D}) k_{B} p_{B} A_2 \frac{B}{N_1} \\
&\quad - k_{E} p_{E} A_2 \frac{E}{N_2} - (1-k_{E} p_{E}) k_{C} p_{C} A_2 \frac{C}{N_1} \\
&\quad - \mu_{A_2} A_2 + \gamma_{D} D + \gamma_{E} E ,
\end{split}
\begin{split}
\frac{dD}{dt} &= k_{D} p_{D} A_2 \frac{D}{N_2} + (1-k_{D} p_{D}) k_{B} p_{B} A_2 \frac{B}{N_1} \\
&\quad - \phi_{E} D \frac{E}{N_2} - (1-\phi_{E}) \phi_{C} D \frac{C}{N_1} \\
&\quad + \phi_{D} E \frac{D}{N_2} + (1-\phi_{D}) \phi_{B} E \frac{B}{N_1} - \mu_{D} D - \gamma_{D} D ,
\end{split}
\begin{split}
\frac{dE}{dt} &= k_{E} p_{E} A_2 \frac{E}{N_2} + (1-k_{E} p_{E}) k_{C} p_{C} A_2 \frac{C}{N_1} \\
&\quad - \phi_{D} E \frac{D}{N_2} - (1-\phi_{D}) \phi_{B} E \frac{B}{N_1} \\
&\quad + \phi_{E} D \frac{E}{N_2} + (1-\phi_{E}) \phi_{C} D \frac{C}{N_1} - \mu_{E} E - \gamma_{E} E
\end{split}
}
\end{equation}
\end{document}

2. 微调字号替代scriptsize

使用\small（比默认字号小一级，幅度温和）或\scalebox{0.9}自定义缩放比例，避免scriptsize过度缩小：

\documentclass{JASSS}
\usepackage{array}
\usepackage{amsmath,systeme}
\usepackage{tabularx,colortbl}
\usepackage{booktabs}
\usepackage{graphicx} % 用于scalebox
\newcolumntype{M}[1]{p{#1}}
\begin{document}
% 方法1：用small环境
\begin{small}
\begin{equation}
\systeme{
\frac{dA_1}{dt}= \mu_1 N_1 - k_{B} p_{B} A_1 \frac{B}{N_1} - (1-k_{B} p_{B}) k_{D} p_{D} A_1 \frac{D}{N_2} - k_{C} p_{C} A_1 \frac{C}{N_1} - (1-k_{C} p_{C}) k_{E} p_{E} A_1 \frac{E}{N_2} - \mu_{A_1} A_1 + \gamma_{B} B + \gamma_{C} C ,  
\frac{dB}{dt}= k_{B} p_{B} A_1 \frac{B}{N_1} + (1-k_{B} p_{B}) k_{D} p_{D} A_1 \frac{D}{N_2} - \phi_{C} B \frac{C}{N_1} - (1-\phi_{C}) \phi_{E} B \frac{E}{N_2} + \phi_{B} C \frac{B}{N_1} + (1-\phi_{B}) \phi_{D} C \frac{D}{N_2} - \mu_{B} B - \gamma_{B} B ,
\frac{dC}{dt}= k_{C} p_{C} A_1 \frac{C}{N_1} + (1-k_{C} p_{C}) k_{E} p_{E} A_1 \frac{E}{N_2} - \phi_{B} C \frac{B}{N_1} - (1-\phi_{B}) \phi_{D} C \frac{D}{N_2} + \phi_{C} B \frac{C}{N_1} + (1-\phi_{C}) \phi_{E} B \frac{E}{N_2} - \mu_{C} C - \gamma_{C} C ,
\frac{dA_2}{dt}=\mu_2 N_2 - k_{D} p_{D} A_2 \frac{D}{N_2} - (1-k_{D} p_{D}) k_{B} p_{B} A_2 \frac{B}{N_1} - k_{E} p_{E} A_2 \frac{E}{N_2} - (1-k_{E} p_{E}) k_{C} p_{C} A_2 \frac{C}{N_1} - \mu_{A_2} A_2 + \gamma_{D} D + \gamma_{E} E ,
\frac{dD}{dt}= k_{D} p_{D} A_2 \frac{D}{N_2} + (1-k_{D} p_{D}) k_{B} p_{B} A_2 \frac{B}{N_1} - \phi_{E} D \frac{E}{N_2} - (1-\phi_{E}) \phi_{C} D \frac{C}{N_1} + \phi_{D} E \frac{D}{N_2} + (1-\phi_{D}) \phi_{B} E \frac{B}{N_1} - \mu_{D} D - \gamma_{D} D ,
\frac{dE}{dt}= k_{E} p_{E} A_2 \frac{E}{N_2} + (1-k_{E} p_{E}) k_{C} p_{C} A_2 \frac{C}{N_1} - \phi_{D} E \frac{D}{N_2} - (1-\phi_{D}) \phi_{B} E \frac{B}{N_1} + \phi_{E} D \frac{E}{N_2} + (1-\phi_{E}) \phi_{C} D \frac{C}{N_1} - \mu_{E} E - \gamma_{E} E }
\end{equation}
\end{small}

% 方法2：自定义缩放比例
\begin{equation}
\scalebox{0.9}{
\systeme{
\frac{dA_1}{dt}= \mu_1 N_1 - k_{B} p_{B} A_1 \frac{B}{N_1} - (1-k_{B} p_{B}) k_{D} p_{D} A_1 \frac{D}{N_2} - k_{C} p_{C} A_1 \frac{C}{N_1} - (1-k_{C} p_{C}) k_{E} p_{E} A_1 \frac{E}{N_2} - \mu_{A_1} A_1 + \gamma_{B} B + \gamma_{C} C ,  
\frac{dB}{dt}= k_{B} p_{B} A_1 \frac{B}{N_1} + (1-k_{B} p_{B}) k_{D} p_{D} A_1 \frac{D}{N_2} - \phi_{C} B \frac{C}{N_1} - (1-\phi_{C}) \phi_{E} B \frac{E}{N_2} + \phi_{B} C \frac{B}{N_1} + (1-\phi_{B}) \phi_{D} C \frac{D}{N_2} - \mu_{B} B - \gamma_{B} B ,
\frac{dC}{dt}= k_{C} p_{C} A_1 \frac{C}{N_1} + (1-k_{C} p_{C}) k_{E} p_{E} A_1 \frac{E}{N_2} - \phi_{B} C \frac{B}{N_1} - (1-\phi_{B}) \phi_{D} C \frac{D}{N_2} + \phi_{C} B \frac{C}{N_1} + (1-\phi_{C}) \phi_{E} B \frac{E}{N_2} - \mu_{C} C - \gamma_{C} C ,
\frac{dA_2}{dt}=\mu_2 N_2 - k_{D} p_{D} A_2 \frac{D}{N_2} - (1-k_{D} p_{D}) k_{B} p_{B} A_2 \frac{B}{N_1} - k_{E} p_{E} A_2 \frac{E}{N_2} - (1-k_{E} p_{E}) k_{C} p_{C} A_2 \frac{C}{N_1} - \mu_{A_2} A_2 + \gamma_{D} D + \gamma_{E} E ,
\frac{dD}{dt}= k_{D} p_{D} A_2 \frac{D}{N_2} + (1-k_{D} p_{D}) k_{B} p_{B} A_2 \frac{B}{N_1} - \phi_{E} D \frac{E}{N_2} - (1-\phi_{E}) \phi_{C} D \frac{C}{N_1} + \phi_{D} E \frac{D}{N_2} + (1-\phi_{D}) \phi_{B} E \frac{B}{N_1} - \mu_{D} D - \gamma_{D} D ,
\frac{dE}{dt}= k_{E} p_{E} A_2 \frac{E}{N_2} + (1-k_{E} p_{E}) k_{C} p_{C} A_2 \frac{C}{N_1} - \phi_{D} E \frac{D}{N_2} - (1-\phi_{D}) \phi_{B} E \frac{B}{N_1} + \phi_{E} D \frac{E}{N_2} + (1-\phi_{E}) \phi_{C} D \frac{C}{N_1} - \mu_{E} E - \gamma_{E} E }
}
\end{equation}
\end{document}

3. 优化公式紧凑性

将分式改为行内形式（如$\frac{B}{N_1}$改为$B/N_1$），或定义重复项的缩写命令，减少横向空间占用：

\documentclass{JASSS}
\usepackage