How to adjust the blank space between the top of the left curly brace and the contents?

Question

I want to type a system of equations delimited by the left curly brace. And I tried using the \left{ with aligned, and cases, and array, and numcases. But there are some difference between the results of these four methods. Here is the screen-shots and the source file:

\documentclass{article}

\usepackage{amsmath,amssymb,cases}

\begin{document}
      \begin{align*}
     &\left\{\begin{aligned}
       &x=x,\\
        &u=u(x,t).
          \end{aligned}\right.   
          ~~~&& \begin{cases}
         x=x,\\
          u=u(x,t).
          \end{cases}
         ~~ &&
           \left\{\begin{array}{l}
         x=x,\\
      u=u(x,t).
        \end{array}\right.\\
      &\text{align} && \text{cases} &&\text{array}     
       \end{align*}

       using numcases:
      \begin{numcases}{}
        x=x,\nonumber\\
         u=u(x,t). \nonumber
      \end{numcases}
\end{document}

My question is how can I adjust the space between the top tip of left curly brace and the first line of the equations, so that the results of using array etc is the same as that of using numcases. At present, I have no way of doing this.

When I tried using scalerel.sty, the result is as above: I do not know why? May be I was wrong in installing the scalerel.sty.

Answer 1

I would say that with numcases the brace is a bit too low. Nevertheless, I fully agree that the braces with aligned and cases are much too large. Here's what I often do as a remedy:

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\def\env@cases{%
  \let\@ifnextchar\new@ifnextchar
  \left\lbrace
  \def\arraystretch{1.1}%
  \array{@{\,}l@{\quad}l@{}}%
}
\makeatother
\begin{document}
\[
  \begin{cases}
    x=x, \\
    u=u(x,t).
  \end{cases}
  \quad
  \begin{cases}
    a=a, \\
    x=x, \\
    u=u(x,t).
  \end{cases}
  \quad
  \begin{cases}
    a=a, \\
    b=b, \\
    x=x, \\
    u=u(x,t).
  \end{cases}
\]
\end{document}

The point is that amsmath's cases uses an \arraystretch of 1.2, which doesn't work well with TeX's standard brace sizes. I prefer using 1.1 instead of 1.2; of course this means that there's a bit less vertical space between the cases. Maybe you'll deem the braces still too large, but in my opinion this is a good compromise. (The distance to the brace tips appears a bit large only because a, x and u don't have ascenders and descenders.)

Answer 2

The \! macro does a thin backspace. I have placed them through your MWE with prejudice to demonstrate where they might go.

\documentclass{article}
\usepackage{amsmath,amssymb}
  \usepackage{cases}
 \begin{document}
  \begin{align*}
 &\left\{\!\!\begin{aligned}
   &x=x,\\
    &u=u(x,t).
      \end{aligned}\right.   
      ~~~&& \begin{cases}
     \!\!x=x,\\
      \!\!u=u(x,t).
      \end{cases}
     ~~ &&
       \left\{\!\!\!\!\begin{array}{l}
     x=x,\\
  u=u(x,t).
    \end{array}\right.\\
  &\text{align} && \text{cases} &&\text{array}     
   \end{align*}

   using numcases:
  \begin{numcases}{}
    \!\!\!x=x,\nonumber\\
    \!\!\! u=u(x,t). \nonumber
              \end{numcases}
  \end{document}

If the approximate space gotten by this method is insufficiently accurate, one could use \rule{length}{0ex} to get a more precise space, where length can be positive or negative.

EDITED to adjust vertical extent of braces:

\documentclass{article}
\usepackage{scalerel}
\usepackage{verbatimbox}
\usepackage{amsmath,amssymb,cases}

\begin{document}

\def\x{\mbox{\addvbuffer[-0.8ex -.1ex]{$\begin{aligned}
       &x=x,\\
        &u=u(x,t).
          \end{aligned}$}}
}
\def\z{\mbox{\addvbuffer[-0.8ex -.1ex]{$\begin{array}{l}
       x=x,\\
        u=u(x,t).
          \end{array}$}}
}
      \begin{align*}
     &\scaleleftright[1.7ex]{\{}{\x}{.}
          ~~~&&  \begin{cases}
     \x
      \end{cases}
         ~~ &&
     \scaleleftright[1.7ex]{\{}{\z}{.}
        \\
      &\text{align} && \text{cases} &&\text{array}     
       \end{align*}

       using numcases:
      \begin{numcases}{}
        x=x,\nonumber\\
         u=u(x,t). \nonumber
      \end{numcases}

\end{document}