Alternative ways to format the cases environment in display math-mode

Question

The cases environment of amsmath package is useful for defining a function that takes different values in different regions. For example:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
f(x) = \begin{cases}
        g_1(x), & \text{if condition 1}; \\
        g_2(x), & \text{if condition 2}; \\
        g_3(x), & \text{if condition 3}; \\
        g_4(x), & \text{if condition 4}; \\
        g_5(x), & \text{if condition 5}; \\
        g_6(x), & \text{if condition 6}; \\
        g_7(x), & \text{if condition 7}. \\
       \end{cases}
\end{equation}
\end{document}

For such long expressions, the cases environment is easy to read; however, it takes too much vertical space (and for journal and conference papers, space is always at a premium). Is there any alternative way to format such expression that is readable but takes less space than cases environment?

Answer 1

cases sets \arraystretch to 1.2. You can decrease this value:

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\def\env@cases{%
  \let\@ifnextchar\new@ifnextchar
  \left\lbrace
  \def\arraystretch{1}%
  \array{@{}l@{\quad}l@{}}}
\makeatother
\begin{document}
\begin{equation}
f(x) = \begin{cases}
        g_1(x), & \text{if condition 1}; \\
        g_2(x), & \text{if condition 2}; \\
        g_3(x), & \text{if condition 3}; \\
        g_4(x), & \text{if condition 4}; \\
        g_5(x), & \text{if condition 5}; \\
        g_6(x), & \text{if condition 6}; \\
        g_7(x), & \text{if condition 7}. \\
       \end{cases}
\end{equation}
\end{document}